Chen, Changkai; Zhang, Xiaohua; Liu, Zhang A high-order compact finite difference scheme and precise integration method based on modified Hopf-Cole transformation for numerical simulation of \(n\)-dimensional Burgers’ system. (English) Zbl 1433.65156 Appl. Math. Comput. 372, Article ID 125009, 28 p. (2020). MSC: 65M06 35K51 35Q53 65M70 PDF BibTeX XML Cite \textit{C. Chen} et al., Appl. Math. Comput. 372, Article ID 125009, 28 p. (2020; Zbl 1433.65156) Full Text: DOI
Yang, Mei; Zhao, Fengqun; Guo, Chong The sinc-Galerkin methods of the Burgers’ equation based on the Hopf-Cole transformation. (Chinese. English summary) Zbl 1449.65265 Chin. J. Comput. Mech. 36, No. 6, 807-812 (2019). MSC: 65M60 65D05 35Q53 PDF BibTeX XML Cite \textit{M. Yang} et al., Chin. J. Comput. Mech. 36, No. 6, 807--812 (2019; Zbl 1449.65265) Full Text: DOI
Léger, Flavien; Li, Wuchen Hopf-Cole transformation and Schrödinger problems. (English) Zbl 07178768 Nielsen, Frank (ed.) et al., Geometric science of information. 4th international conference, GSI 2019, Toulouse, France, August 27–29, 2019. Proceedings. Cham: Springer (ISBN 978-3-030-26979-1/pbk; 978-3-030-26980-7/ebook). Lecture Notes in Computer Science 11712, 733-738 (2019). MSC: 94A08 94A12 94A15 94A17 PDF BibTeX XML Cite \textit{F. Léger} and \textit{W. Li}, Lect. Notes Comput. Sci. 11712, 733--738 (2019; Zbl 07178768) Full Text: DOI
Jensen, Max; Majee, Ananta K.; Prohl, Andreas; Schellnegger, Christian Dynamic programming for finite ensembles of nanomagnetic particles. (English) Zbl 07086340 J. Sci. Comput. 80, No. 1, 351-375 (2019). MSC: 45K05 46S50 49L20 49L25 91A23 93E20 PDF BibTeX XML Cite \textit{M. Jensen} et al., J. Sci. Comput. 80, No. 1, 351--375 (2019; Zbl 07086340) Full Text: DOI
Zhang, Rongpei; Wang, Di; Liu, Jia LDG method for solving Burger’s equation based on generalized alternating numerical fluxes. (Chinese. English summary) Zbl 1424.65176 J. Shenyang Norm. Univ., Nat. Sci. 36, No. 5, 424-429 (2018). MSC: 65M60 65M12 PDF BibTeX XML Cite \textit{R. Zhang} et al., J. Shenyang Norm. Univ., Nat. Sci. 36, No. 5, 424--429 (2018; Zbl 1424.65176) Full Text: DOI
Gao, Q.; Zou, M. Y. An analytical solution for two and three dimensional nonlinear Burgers’ equation. (English) Zbl 1446.35172 Appl. Math. Modelling 45, 255-270 (2017). MSC: 35Q53 PDF BibTeX XML Cite \textit{Q. Gao} and \textit{M. Y. Zou}, Appl. Math. Modelling 45, 255--270 (2017; Zbl 1446.35172) Full Text: DOI
Luo, Songting; Payne, Nicholas Properties-preserving high order numerical methods for a kinetic eikonal equation. (English) Zbl 1380.65163 J. Comput. Phys. 331, 73-89 (2017). MSC: 65M06 65M12 PDF BibTeX XML Cite \textit{S. Luo} and \textit{N. Payne}, J. Comput. Phys. 331, 73--89 (2017; Zbl 1380.65163) Full Text: DOI
Luo, Songting; Payne, Nicholas An asymptotic method based on a Hopf-Cole transformation for a kinetic BGK equation in the hyperbolic limit. (English) Zbl 1376.76057 J. Comput. Phys. 341, 295-312 (2017). MSC: 76P05 82C40 35Q35 76M20 65M06 82C80 PDF BibTeX XML Cite \textit{S. Luo} and \textit{N. Payne}, J. Comput. Phys. 341, 295--312 (2017; Zbl 1376.76057) Full Text: DOI
Tsai, Chih-Ching; Shih, Yin-Tzer; Lin, Yu-Tuan; Wang, Hui-Ching Tailored finite point method for solving one-dimensional Burgers’ equation. (English) Zbl 1364.65219 Int. J. Comput. Math. 94, No. 4, 800-812 (2017). MSC: 65M99 35Q35 35K55 PDF BibTeX XML Cite \textit{C.-C. Tsai} et al., Int. J. Comput. Math. 94, No. 4, 800--812 (2017; Zbl 1364.65219) Full Text: DOI
Caillerie, Nils Large deviations of a velocity jump process with a Hamilton-Jacobi approach. (Grandes déviations pour un processus à sauts de vitesse avec une approche de Hamilton-Jacobi.) (English. Abridged French version) Zbl 1364.60034 C. R., Math., Acad. Sci. Paris 355, No. 2, 170-175 (2017). Reviewer: Dominique Lepingle (Orléans) MSC: 60F10 60J75 60H15 49L25 PDF BibTeX XML Cite \textit{N. Caillerie}, C. R., Math., Acad. Sci. Paris 355, No. 2, 170--175 (2017; Zbl 1364.60034) Full Text: DOI
Chen, Yang; Fan, Engui; Yuen, Manwai The Hopf-Cole transformation, topological solitons and multiple fusion solutions for the \(n\)-dimensional Burgers system. (English) Zbl 1377.35055 Phys. Lett., A 380, No. 1-2, 9-14 (2016). MSC: 35C08 35Q51 37K40 35Q53 PDF BibTeX XML Cite \textit{Y. Chen} et al., Phys. Lett., A 380, No. 1--2, 9--14 (2016; Zbl 1377.35055) Full Text: DOI
Gao, Wei; Zhang, Bao; Li, Hong; Liu, Yang A high-order compact finite volume method for solving Burgers equations. (Chinese. English summary) Zbl 1363.65143 Math. Appl. 29, No. 2, 331-339 (2016). MSC: 65M08 35Q53 65M12 65M20 65L06 65M15 PDF BibTeX XML Cite \textit{W. Gao} et al., Math. Appl. 29, No. 2, 331--339 (2016; Zbl 1363.65143)
Zheng, Quan; Liu, Yufeng; Fan, Lei A finite difference method for Burgers’ equation in the unbounded domain using artificial boundary conditions. (English) Zbl 1338.65218 J. Comput. Anal. Appl. 20, No. 1, 140-150 (2016). Reviewer: Seenith Sivasundaram (Daytona Beach) MSC: 65M06 35Q53 65M12 PDF BibTeX XML Cite \textit{Q. Zheng} et al., J. Comput. Anal. Appl. 20, No. 1, 140--150 (2016; Zbl 1338.65218)
Vasil’ev, G. S.; Imomnazarov, Kh. Kh.; Mamasoliev, B. J. On one system of the Burgers equations arising in the two-velocity hydrodynamics. (English) Zbl 1374.76015 Bull. Novosib. Comput. Cent., Ser. Numer. Model. Atmos. Ocean Environ. Stud. 15, 67-76 (2015). MSC: 76A05 35Q35 PDF BibTeX XML Cite \textit{G. S. Vasil'ev} et al., Bull. Novosib. Comput. Cent., Ser. Numer. Model. Atmos. Ocean Environ. Stud. 15, 67--76 (2015; Zbl 1374.76015) Full Text: Link
Zhao, Guozhong; Yu, Xijun Direct discontinuous Galerkin finite element methods based on the Hopf-Cole transformation for solving a kind of Burgers equations. (Chinese. English summary) Zbl 1349.65499 Numer. Math., Nanjing 37, No. 2, 141-155 (2015). MSC: 65M60 35Q53 35K05 PDF BibTeX XML Cite \textit{G. Zhao} and \textit{X. Yu}, Numer. Math., Nanjing 37, No. 2, 141--155 (2015; Zbl 1349.65499)
Prakash, B. Mayur; Awasthi, Ashish; Jayaraj, S. A numerical simulation based on modified Keller box scheme for fluid flow: the unsteady viscous Burgers’ equation. (English) Zbl 1381.76239 Agrawal, P. N. (ed.) et al., Mathematical analysis and its applications. Proceedings of the international conference on recent trends in mathematical analyis and its applications, ICRTMAA 2014, Roorkee, India, December 21–23, 2014. New Delhi: Springer (ISBN 978-81-322-2484-6/hbk; 978-81-322-2485-3/ebook). Springer Proceedings in Mathematics & Statistics 143, 565-575 (2015). MSC: 76M20 65M06 35Q53 PDF BibTeX XML Cite \textit{B. M. Prakash} et al., in: Mathematical analysis and its applications. Proceedings of the international conference on recent trends in mathematical analyis and its applications, ICRTMAA 2014, Roorkee, India, December 21--23, 2014. New Delhi: Springer. 565--575 (2015; Zbl 1381.76239) Full Text: DOI
Bouin, Emeric A Hamilton-Jacobi approach for front propagation in kinetic equations. (English) Zbl 1329.35317 Kinet. Relat. Models 8, No. 2, 255-280 (2015). MSC: 35Q92 45K05 35C07 35F21 35P25 92D25 35D40 35B50 PDF BibTeX XML Cite \textit{E. Bouin}, Kinet. Relat. Models 8, No. 2, 255--280 (2015; Zbl 1329.35317) Full Text: DOI
Verma, Amit K.; Verma, Lajja Higher order time integration formula with application on Burgers’ equation. (English) Zbl 1318.65036 Int. J. Comput. Math. 92, No. 4, 756-771 (2015). MSC: 65L05 34A34 65M20 35Q53 65L20 65L70 PDF BibTeX XML Cite \textit{A. K. Verma} and \textit{L. Verma}, Int. J. Comput. Math. 92, No. 4, 756--771 (2015; Zbl 1318.65036) Full Text: DOI
Zheng, Quan; Fan, Lei; Li, Xuezheng An artificial boundary method for Burgers equation in the unbounded domain. (English) Zbl 1357.65140 CMES, Comput. Model. Eng. Sci. 100, No. 6, 445-461 (2014). MSC: 65M06 65M12 35Q53 PDF BibTeX XML Cite \textit{Q. Zheng} et al., CMES, Comput. Model. Eng. Sci. 100, No. 6, 445--461 (2014; Zbl 1357.65140) Full Text: DOI
Anikonov, Yu. E.; Ayupova, N. B. The Hopf-Cole transformation and multidimensional representations of solutions to evolution equations. (Russian, English) Zbl 1340.35379 Sib. Zh. Ind. Mat. 17, No. 4, 31-37 (2014); translation in J. Appl. Ind. Math. 9, No. 1, 11-17 (2015). MSC: 35R30 35C05 PDF BibTeX XML Cite \textit{Yu. E. Anikonov} and \textit{N. B. Ayupova}, Sib. Zh. Ind. Mat. 17, No. 4, 31--37 (2014; Zbl 1340.35379); translation in J. Appl. Ind. Math. 9, No. 1, 11--17 (2015) Full Text: DOI
Kaysar, Rahman; Helil, Nurmamat A high-order compact Padé approximation scheme for solving Burgers equation. (Chinese. English summary) Zbl 1324.65112 J. Henan Norm. Univ., Nat. Sci. 42, No. 4, 6-12 (2014). MSC: 65M06 65M12 35Q53 PDF BibTeX XML Cite \textit{R. Kaysar} and \textit{N. Helil}, J. Henan Norm. Univ., Nat. Sci. 42, No. 4, 6--12 (2014; Zbl 1324.65112)
Li, Jingyu; Li, Tong; Wang, Zhi-An Stability of traveling waves of the Keller-Segel system with logarithmic sensitivity. (English) Zbl 1311.35021 Math. Models Methods Appl. Sci. 24, No. 14, 2819 (2014). Reviewer: Peixuan Weng (Guangzhou) MSC: 35B35 35K55 92C17 35C07 PDF BibTeX XML Cite \textit{J. Li} et al., Math. Models Methods Appl. Sci. 24, No. 14, 2819 (2014; Zbl 1311.35021) Full Text: DOI
Pocheketa, Oleksandr A. Normalized classes of generalized Burgers equations. (English) Zbl 1292.35017 Vaneeva, O. O. (ed.) et al., Proceedings of the 6th international workshop on group analysis of differential equations and integrable systems, Protaras, Cyprus, June 17–21, 2012. Nicosia: University of Cyprus, Department of Mathematics and Statistics (ISBN 978-9963-700-63-9/pbk). 170-178 (2013). MSC: 35B06 35K58 PDF BibTeX XML Cite \textit{O. A. Pocheketa}, in: Proceedings of the 6th international workshop on group analysis of differential equations and integrable systems, Protaras, Cyprus, June 17--21, 2012. Nicosia: University of Cyprus, Department of Mathematics and Statistics. 170--178 (2013; Zbl 1292.35017) Full Text: arXiv
Jin, Hai-Yang; Li, Jingyu; Wang, Zhi-An Asymptotic stability of traveling waves of a chemotaxis model with singular sensitivity. (English) Zbl 1293.35071 J. Differ. Equations 255, No. 2, 193-219 (2013). Reviewer: Yaping Liu (Pittsburg) MSC: 35C07 35K55 46N60 92C17 35B35 PDF BibTeX XML Cite \textit{H.-Y. Jin} et al., J. Differ. Equations 255, No. 2, 193--219 (2013; Zbl 1293.35071) Full Text: DOI
Ozawa, Tohru; Sunagawa, Hideaki Small data blow-up for a system of nonlinear Schrödinger equations. (English) Zbl 1256.35107 J. Math. Anal. Appl. 399, No. 1, 147-155 (2013). MSC: 35Q41 35B44 PDF BibTeX XML Cite \textit{T. Ozawa} and \textit{H. Sunagawa}, J. Math. Anal. Appl. 399, No. 1, 147--155 (2013; Zbl 1256.35107) Full Text: DOI arXiv
Wu, Wenjuan; Feng, Xinlong; Liu, Demin The local discontinuous Galerkin finite element method for a class of convection-diffusion equations. (English) Zbl 1259.65153 Nonlinear Anal., Real World Appl. 14, No. 1, 734-752 (2013). Reviewer: Wilhelm Heinrichs (Essen) MSC: 65M60 35K20 65M12 65M15 PDF BibTeX XML Cite \textit{W. Wu} et al., Nonlinear Anal., Real World Appl. 14, No. 1, 734--752 (2013; Zbl 1259.65153) Full Text: DOI
Kweyu, M. C.; Manyonge, W. A.; Koross, Alfred K.; Ssemaganda, Vincent Numerical solutions of the Burgers system in two dimensions under varied initial and boundary conditions. (English) Zbl 1262.65105 Appl. Math. Sci., Ruse 6, No. 113-116, 5603-5615 (2012). MSC: 65M06 PDF BibTeX XML Cite \textit{M. C. Kweyu} et al., Appl. Math. Sci., Ruse 6, No. 113--116, 5603--5615 (2012; Zbl 1262.65105) Full Text: Link
Guéant, Olivier New numerical methods for mean field games with quadratic costs. (English) Zbl 1270.35020 Netw. Heterog. Media 7, No. 2, 315-336 (2012). MSC: 35A35 35K91 65M12 91A15 35R60 PDF BibTeX XML Cite \textit{O. Guéant}, Netw. Heterog. Media 7, No. 2, 315--336 (2012; Zbl 1270.35020) Full Text: DOI
Mirrahimi, Sepideh; Barles, Guy; Perthame, Benoît; Souganidis, Panagiotis E. A singular Hamilton-Jacobi equation modeling the tail problem. (English) Zbl 1280.35007 SIAM J. Math. Anal. 44, No. 6, 4297-4319 (2012). Reviewer: Georgii Sviridyuk (Chelyabinsk) MSC: 35B25 35K57 49L25 92D15 35F21 35B40 PDF BibTeX XML Cite \textit{S. Mirrahimi} et al., SIAM J. Math. Anal. 44, No. 6, 4297--4319 (2012; Zbl 1280.35007) Full Text: DOI
Tian, Shou-Fu; Zhou, Sheng-Wu; Jiang, Wu-You; Zhang, Hong-Qing Analytic solutions, Darboux transformation operators and supersymmetry for a generalized one-dimensional time-dependent Schrödinger equation. (English) Zbl 1252.35239 Appl. Math. Comput. 218, No. 13, 7308-7321 (2012). MSC: 35Q41 35A22 81Q05 PDF BibTeX XML Cite \textit{S.-F. Tian} et al., Appl. Math. Comput. 218, No. 13, 7308--7321 (2012; Zbl 1252.35239) Full Text: DOI
Bouin, Emeric; Calvez, Vincent A kinetic eikonal equation. (English. Abridged French version) Zbl 1252.35124 C. R., Math., Acad. Sci. Paris 350, No. 5-6, 243-248 (2012). Reviewer: Pau Martin de la Torre (Barcelona) MSC: 35F21 35D40 PDF BibTeX XML Cite \textit{E. Bouin} and \textit{V. Calvez}, C. R., Math., Acad. Sci. Paris 350, No. 5--6, 243--248 (2012; Zbl 1252.35124) Full Text: DOI
Shao, Long; Feng, Xinlong; He, Yinnian The local discontinuous Galerkin finite element method for Burger’s equation. (English) Zbl 1235.65115 Math. Comput. Modelling 54, No. 11-12, 2943-2954 (2011). MSC: 65M12 65M60 35Q53 PDF BibTeX XML Cite \textit{L. Shao} et al., Math. Comput. Modelling 54, No. 11--12, 2943--2954 (2011; Zbl 1235.65115) Full Text: DOI
Zhao, Guozhong; Yu, Xijun; Zhang, Rongpei The new numerical method for solving the system of two-dimensional Burgers equations. (English) Zbl 1232.65133 Comput. Math. Appl. 62, No. 8, 3279-3291 (2011). MSC: 65M60 35Q53 PDF BibTeX XML Cite \textit{G. Zhao} et al., Comput. Math. Appl. 62, No. 8, 3279--3291 (2011; Zbl 1232.65133) Full Text: DOI
Pandey, K.; Verma, Lajja; Verma, Amit K. \(L\)-stable Simpson’s 3/8 rule and Burgers’ equation. (English) Zbl 1229.65188 Appl. Math. Comput. 218, No. 4, 1342-1352 (2011). MSC: 65M70 35Q53 35K05 65M12 PDF BibTeX XML Cite \textit{K. Pandey} et al., Appl. Math. Comput. 218, No. 4, 1342--1352 (2011; Zbl 1229.65188) Full Text: DOI
Matskevich, S. E. Burgers equation and Kolmogorov-Petrovsky-Piskunov equation on manifolds. (English) Zbl 1221.35208 Infin. Dimens. Anal. Quantum Probab. Relat. Top. 14, No. 2, 199-208 (2011). MSC: 35K58 35A22 58J35 PDF BibTeX XML Cite \textit{S. E. Matskevich}, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 14, No. 2, 199--208 (2011; Zbl 1221.35208) Full Text: DOI
Keanini, R. G. Green’s function-stochastic methods framework for probing nonlinear evolution problems: Burger’s equation, the nonlinear Schrödinger’s equation, and hydrodynamic organization of near-molecular-scale vorticity. (English) Zbl 1223.35280 Ann. Phys. 326, No. 4, 1002-1031 (2011). Reviewer: René L. Schilling (Dresden) MSC: 35Q53 35A08 60H15 35Q55 35Q84 PDF BibTeX XML Cite \textit{R. G. Keanini}, Ann. Phys. 326, No. 4, 1002--1031 (2011; Zbl 1223.35280) Full Text: DOI arXiv
Zumbrun, Kevin Instantaneous shock location and one-dimensional nonlinear stability of viscous shock waves. (English) Zbl 1221.35059 Q. Appl. Math. 69, No. 1, 177-202 (2011). Reviewer: Michael I. Gil’ (Beer-Sheva) MSC: 35B35 35L67 35A22 PDF BibTeX XML Cite \textit{K. Zumbrun}, Q. Appl. Math. 69, No. 1, 177--202 (2011; Zbl 1221.35059) Full Text: DOI Link arXiv
Asokan, R. A Bäcklund transformations for \(u_y+\alpha u_{xx}+\beta u_{xxx} = f(x,y,u,u_x)\). (English) Zbl 1399.35328 Int. Electron. J. Pure Appl. Math. 1, No. 2, 177-194 (2010). MSC: 35Q55 35Q41 35J10 35K05 PDF BibTeX XML Cite \textit{R. Asokan}, Int. Electron. J. Pure Appl. Math. 1, No. 2, 177--194 (2010; Zbl 1399.35328) Full Text: Link
Scimiterna, Christian; Levi, Decio \(C\)-integrability test for discrete equations via multiple scale expansions. (English) Zbl 1219.39002 SIGMA, Symmetry Integrability Geom. Methods Appl. 6, Paper 070, 17 p. (2010). MSC: 39A12 39A10 34K99 34E13 37J30 37K10 PDF BibTeX XML Cite \textit{C. Scimiterna} and \textit{D. Levi}, SIGMA, Symmetry Integrability Geom. Methods Appl. 6, Paper 070, 17 p. (2010; Zbl 1219.39002) Full Text: DOI EuDML arXiv
Liu, Tai-Ping; Yu, Shih-Hsien Viscous rarefaction waves. (English) Zbl 1216.35120 Bull. Inst. Math., Acad. Sin. (N.S.) 5, No. 2, 123-179 (2010). Reviewer: Boris V. Loginov (Ul’yanovsk) MSC: 35Q53 76N15 76D33 37N10 37K35 PDF BibTeX XML Cite \textit{T.-P. Liu} and \textit{S.-H. Yu}, Bull. Inst. Math., Acad. Sin. (N.S.) 5, No. 2, 123--179 (2010; Zbl 1216.35120)
Liao, Wenyuan A fourth-order finite-difference method for solving the system of two-dimensional Burgers’ equations. (English) Zbl 1377.65108 Int. J. Numer. Methods Fluids 64, No. 5, 565-590 (2010). MSC: 65M06 76M20 PDF BibTeX XML Cite \textit{W. Liao}, Int. J. Numer. Methods Fluids 64, No. 5, 565--590 (2010; Zbl 1377.65108) Full Text: DOI
Strömberg, Thomas On a viscous Hamilton-Jacobi equation with an unbounded potential term. (English) Zbl 1197.35080 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 73, No. 6, 1802-1811 (2010). MSC: 35F21 35A01 35A02 35C15 35B51 PDF BibTeX XML Cite \textit{T. Strömberg}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 73, No. 6, 1802--1811 (2010; Zbl 1197.35080) Full Text: DOI
Zhao, Guo-Zhong; Yu, Xi-Jun; Wu, Di Numerical solution of the Burgers’ equation by local discontinuous Galerkin method. (English) Zbl 1195.65132 Appl. Math. Comput. 216, No. 12, 3671-3679 (2010). MSC: 65M60 35Q53 65L06 PDF BibTeX XML Cite \textit{G.-Z. Zhao} et al., Appl. Math. Comput. 216, No. 12, 3671--3679 (2010; Zbl 1195.65132) Full Text: DOI
Xie, Shusen; Li, Guangxing; Yi, Sucheol; Heo, Sunyeong A compact finite difference method for solving Burgers’ equation. (English) Zbl 1213.65120 Int. J. Numer. Methods Fluids 62, No. 7, 747-764 (2010). Reviewer: Maria Christina Mariani (El Paso) MSC: 65M06 65M12 35Q53 PDF BibTeX XML Cite \textit{S. Xie} et al., Int. J. Numer. Methods Fluids 62, No. 7, 747--764 (2010; Zbl 1213.65120) Full Text: DOI
Pandey, K.; Verma, Lajja; Verma, Amit K. On a finite difference scheme for Burgers’ equation. (English) Zbl 1178.65103 Appl. Math. Comput. 215, No. 6, 2206-2214 (2009). MSC: 65M06 35Q53 65M12 65M15 PDF BibTeX XML Cite \textit{K. Pandey} et al., Appl. Math. Comput. 215, No. 6, 2206--2214 (2009; Zbl 1178.65103) Full Text: DOI
Salkuyeh, D. Khojasteh; Sharafeh, F. Saadati On the numerical solution of the Burgers’s equation. (English) Zbl 1172.65055 Int. J. Comput. Math. 86, No. 8, 1334-1344 (2009). Reviewer: Iwan Gawriljuk (Eisenach) MSC: 65M20 65M06 35K05 35Q53 PDF BibTeX XML Cite \textit{D. K. Salkuyeh} and \textit{F. S. Sharafeh}, Int. J. Comput. Math. 86, No. 8, 1334--1344 (2009; Zbl 1172.65055) Full Text: DOI
Liao, Wenyuan An implicit fourth-order compact finite difference scheme for one-dimensional Burgers’ equation. (English) Zbl 1157.65438 Appl. Math. Comput. 206, No. 2, 755-764 (2008). MSC: 65M06 65M12 35Q53 PDF BibTeX XML Cite \textit{W. Liao}, Appl. Math. Comput. 206, No. 2, 755--764 (2008; Zbl 1157.65438) Full Text: DOI
Xie, Shu-Sen; Heo, Sunyeong; Kim, Seokchan; Woo, Gyungsoo; Yi, Sucheol Numerical solution of one-dimensional Burgers’ equation using reproducing kernel function. (English) Zbl 1140.65069 J. Comput. Appl. Math. 214, No. 2, 417-434 (2008). Reviewer: Aniket Mahanti (Saint John) MSC: 65M60 35Q53 65M12 65M15 46E22 PDF BibTeX XML Cite \textit{S.-S. Xie} et al., J. Comput. Appl. Math. 214, No. 2, 417--434 (2008; Zbl 1140.65069) Full Text: DOI
Bai, Cheng-Lin; Zhao, Hong Infinitely many new solutions and the closed form of the solution for initial-value problem of the Burgers equation. (English) Zbl 1137.35417 Chaos Solitons Fractals 33, No. 4, 1285-1291 (2007). MSC: 35Q53 35C05 35Q51 PDF BibTeX XML Cite \textit{C.-L. Bai} and \textit{H. Zhao}, Chaos Solitons Fractals 33, No. 4, 1285--1291 (2007; Zbl 1137.35417) Full Text: DOI
Lin, P.; Leid, P.; Gao, H. Bilinear control system with the reaction-diffusion term satisfying Newton’s law. (English) Zbl 1110.35026 ZAMM, Z. Angew. Math. Mech. 87, No. 1, 14-23 (2007). Reviewer: Vyacheslav I. Maksimov (Ekaterinburg) MSC: 35K57 35B37 93B05 PDF BibTeX XML Cite \textit{P. Lin} et al., ZAMM, Z. Angew. Math. Mech. 87, No. 1, 14--23 (2007; Zbl 1110.35026) Full Text: DOI
Kadalbajoo, Mohan. K.; Awasthi, A. A numerical method based on Crank-Nicolson scheme for Burgers’ equation. (English) Zbl 1112.65081 Appl. Math. Comput. 182, No. 2, 1430-1442 (2006). Reviewer: Vit Dolejsi (Praha) MSC: 65M06 76M20 35Q53 65M12 PDF BibTeX XML Cite \textit{Mohan. K. Kadalbajoo} and \textit{A. Awasthi}, Appl. Math. Comput. 182, No. 2, 1430--1442 (2006; Zbl 1112.65081) Full Text: DOI
Sun, Haiyan; Xie, Shusen A class of parallel alternating group method for one-dimensional Burgers’ equation. (Chinese. English summary) Zbl 1106.65076 Period. Ocean Univ. China 36, No. 3, Suppl., 215-218 (2006). MSC: 65M06 65M12 65Y05 35Q53 35K05 PDF BibTeX XML Cite \textit{H. Sun} and \textit{S. Xie}, Period. Ocean Univ. China 36, No. 3, 215--218 (2006; Zbl 1106.65076)
Leonenko, N. N.; Ruiz-Medina, M. D. Scaling laws for the multidimensional Burgers equation with quadratic external potential. (English) Zbl 1146.80003 J. Stat. Phys. 124, No. 1, 191-205 (2006). Reviewer: Alain Brillard (Riedisheim) MSC: 80A20 60G60 35Q53 60G15 60H15 PDF BibTeX XML Cite \textit{N. N. Leonenko} and \textit{M. D. Ruiz-Medina}, J. Stat. Phys. 124, No. 1, 191--205 (2006; Zbl 1146.80003) Full Text: DOI
Özis, T.; Esen, A.; Kutluay, S. Numerical solution of Burgers’ equation by quadratic B-spline finite elements. (English) Zbl 1070.65097 Appl. Math. Comput. 165, No. 1, 237-249 (2005). MSC: 65M60 65M12 35Q53 PDF BibTeX XML Cite \textit{T. Özis} et al., Appl. Math. Comput. 165, No. 1, 237--249 (2005; Zbl 1070.65097) Full Text: DOI
Abbasbandy, S.; Darvishi, M. T. A numerical solution of Burgers’ equation by modified Adomian method. (English) Zbl 1060.65649 Appl. Math. Comput. 163, No. 3, 1265-1272 (2005). MSC: 65M70 35Q53 PDF BibTeX XML Cite \textit{S. Abbasbandy} and \textit{M. T. Darvishi}, Appl. Math. Comput. 163, No. 3, 1265--1272 (2005; Zbl 1060.65649) Full Text: DOI
Rodrigo, M.; Mimura, M. On some classes of linearizable reaction-convection-diffusion equations. (English) Zbl 1073.35111 Anal. Appl., Singap. 2, No. 1, 11-19 (2004). MSC: 35K55 35K57 35C05 35A22 PDF BibTeX XML Cite \textit{M. Rodrigo} and \textit{M. Mimura}, Anal. Appl., Singap. 2, No. 1, 11--19 (2004; Zbl 1073.35111) Full Text: DOI
Giga, Yoshikazu; Yamada, Kazuyuki On viscous Burgers-like equations with linearly growing initial data. (English) Zbl 1059.35116 Bol. Soc. Parana. Mat. (3) 20, No. 1-2, 29-50 (2002). MSC: 35Q53 76D03 35K55 PDF BibTeX XML Cite \textit{Y. Giga} and \textit{K. Yamada}, Bol. Soc. Parana. Mat. (3) 20, No. 1--2, 29--50 (2002; Zbl 1059.35116)
Joseph, K. T. Exact solution of a system of generalized Hopf equations. (English) Zbl 1011.35092 Z. Anal. Anwend. 21, No. 3, 669-680 (2002). Reviewer: C.Bouzar (Oran) MSC: 35L60 35D05 35L45 46F30 PDF BibTeX XML Cite \textit{K. T. Joseph}, Z. Anal. Anwend. 21, No. 3, 669--680 (2002; Zbl 1011.35092) Full Text: DOI
Miškinis, P. Some properties of fractional Burgers equation. (English) Zbl 0999.35088 Math. Model. Anal. 7, No. 1, 151-158 (2002). MSC: 35Q53 26A33 37K40 PDF BibTeX XML Cite \textit{P. Miškinis}, Math. Model. Anal. 7, No. 1, 151--158 (2002; Zbl 0999.35088)
Arrigo, D. J.; Hickling, F. On the determining equations for the nonclassical reductions of the heat and Burgers’ equation. (English) Zbl 1009.35005 J. Math. Anal. Appl. 270, No. 2, 582-589 (2002). Reviewer: Boris V.Loginov (Ulyanovsk) MSC: 35A30 37K30 35Q53 58J70 37L20 PDF BibTeX XML Cite \textit{D. J. Arrigo} and \textit{F. Hickling}, J. Math. Anal. Appl. 270, No. 2, 582--589 (2002; Zbl 1009.35005) Full Text: DOI
Smaoui, Nejib; Belgacem, Fethi Connections between the convective diffusion equation and the forced Burgers equation. (English) Zbl 1043.35008 J. Appl. Math. Stochastic Anal. 15, No. 1, 57-75 (2002). MSC: 35A22 35B41 35K57 35Q53 37L25 35Q80 37L30 PDF BibTeX XML Cite \textit{N. Smaoui} and \textit{F. Belgacem}, J. Appl. Math. Stochastic Anal. 15, No. 1, 57--75 (2002; Zbl 1043.35008) Full Text: DOI
Ruiz-Medina, M. D.; Angulo, J. M.; Anh, V. V. Scaling limit solution of a fractional Burgers equation. (English) Zbl 1053.60073 Stochastic Processes Appl. 93, No. 2, 285-300 (2001). Reviewer: Bohdan Maslowski (Praha) MSC: 60H15 60G60 60G12 35R60 60F05 PDF BibTeX XML Cite \textit{M. D. Ruiz-Medina} et al., Stochastic Processes Appl. 93, No. 2, 285--300 (2001; Zbl 1053.60073) Full Text: DOI
Miškinis, P. New exact solutions of one-dimensional inhomogeneous Burgers equation. (English) Zbl 1043.35135 Rep. Math. Phys. 48, No. 1-2, 175-181 (2001). MSC: 35Q53 35C05 37K45 PDF BibTeX XML Cite \textit{P. Miškinis}, Rep. Math. Phys. 48, No. 1--2, 175--181 (2001; Zbl 1043.35135) Full Text: DOI
Belgacem, Fethi; Smaoui, Nejib Interactions of parabolic convective diffusion equations and Navier-Stokes equations connected with population dispersal. (English) Zbl 0988.35071 Commun. Appl. Nonlinear Anal. 8, No. 3, 47-67 (2001). Reviewer: Ruxandra Stavre (Bucureşti) MSC: 35K55 35Q30 PDF BibTeX XML Cite \textit{F. Belgacem} and \textit{N. Smaoui}, Commun. Appl. Nonlinear Anal. 8, No. 3, 47--67 (2001; Zbl 0988.35071)
Wang, Wei-Cheng On \(L^{1}\) convergence rate of viscous and numerical approximate solutions of genuinely nonlinear scalar conservation laws. (English) Zbl 0922.65068 SIAM J. Math. Anal. 30, No. 1, 38-52 (1999). Reviewer: Th.Sonar (Hamburg) MSC: 65M12 65M06 35L65 PDF BibTeX XML Cite \textit{W.-C. Wang}, SIAM J. Math. Anal. 30, No. 1, 38--52 (1999; Zbl 0922.65068) Full Text: DOI
Li, Shuanhu Fourier series solution for an unsaturated flow with extraction. (English) Zbl 0934.35073 Math. Appl. 10, No. 4, 71-75 (1997). MSC: 35K60 35A22 35C10 PDF BibTeX XML Cite \textit{S. Li}, Math. Appl. 10, No. 4, 71--75 (1997; Zbl 0934.35073)
Dermoune, A. Around the stochastic Burgers equations. (English) Zbl 0885.60055 Stochastic Anal. Appl. 15, No. 3, 295-311 (1997). MSC: 60H15 35Q53 PDF BibTeX XML Cite \textit{A. Dermoune}, Stochastic Anal. Appl. 15, No. 3, 295--311 (1997; Zbl 0885.60055) Full Text: DOI
Kifer, Yuri The Burgers equation with a random force and a general model for directed polymers in random environments. (English) Zbl 0883.60059 Probab. Theory Relat. Fields 108, No. 1, 29-65 (1997). MSC: 60H15 60G50 35Q55 35R60 PDF BibTeX XML Cite \textit{Y. Kifer}, Probab. Theory Relat. Fields 108, No. 1, 29--65 (1997; Zbl 0883.60059) Full Text: DOI
Truman, A.; Zhao, H. Z. On stochastic diffusion equations and stochastic Burgers’ equations. (English) Zbl 0866.35149 J. Math. Phys. 37, No. 1, 283-307 (1996). Reviewer: S.Wedrychowicz (Rzeszów) MSC: 35R60 35Q53 35C05 60H15 PDF BibTeX XML Cite \textit{A. Truman} and \textit{H. Z. Zhao}, J. Math. Phys. 37, No. 1, 283--307 (1996; Zbl 0866.35149) Full Text: DOI
Guil, F.; Mañas, M.; Álvarez, G. The Hopf-Cole transformation and the KP equation. (English) Zbl 0961.35504 Phys. Lett., A 190, No. 1, 49-52 (1994). MSC: 35Q53 37K10 PDF BibTeX XML Cite \textit{F. Guil} et al., Phys. Lett., A 190, No. 1, 49--52 (1994; Zbl 0961.35504) Full Text: DOI
Cavalcante, J. A.; Silva, J. A. The equation: \(u_ t=(\frac {u}{2}g(u,u_ x,\dots)+ g(u,u_ x,\dots)_ x)_{_ x}\). (English) Zbl 0843.35097 Appl. Anal. 53, No. 1-2, 107-115 (1994). Reviewer: J.A.Cavalcante (Brasilia) MSC: 35Q53 58J72 PDF BibTeX XML Cite \textit{J. A. Cavalcante} and \textit{J. A. Silva}, Appl. Anal. 53, No. 1--2, 107--115 (1994; Zbl 0843.35097)
Sophocleous, C. A special class of Bäcklund transformations for certain nonlinear partial differential equations. (English) Zbl 0804.35122 Ibragimov, N. Kh. (ed.) et al., Modern group analysis: Advanced analytical and computational methods in mathematical physics. Proceedings of the international workshop Acireale, Catania, Italy, October 27-31, 1992. Dordrecht: Kluwer Academic Publishers. 345-352 (1993). MSC: 35Q53 58J72 PDF BibTeX XML Cite \textit{C. Sophocleous}, in: Modern group analysis: Advanced analytical and computational methods in mathematical physics. Proceedings of the international workshop Acireale, Catania, Italy, October 27-31, 1992. Dordrecht: Kluwer Academic Publishers. 345--352 (1993; Zbl 0804.35122)
Parker, A. On the periodic solution of the Burgers equation: A unified approach. (English) Zbl 0756.35083 Proc. R. Soc. Lond., Ser. A 438, No. 1902, 113-132 (1992). MSC: 35Q53 58J72 35B10 PDF BibTeX XML Cite \textit{A. Parker}, Proc. R. Soc. Lond., Ser. A 438, No. 1902, 113--132 (1992; Zbl 0756.35083) Full Text: DOI
von Wolfersdorf, Lothar On the linearization of the Satsuma-Mimura diffusion equation in the spatial periodic case. (English) Zbl 0764.35050 Z. Anal. Anwend. 10, No. 2, 193-200 (1991). MSC: 35K55 35Q35 45K05 35C10 35C15 35B40 PDF BibTeX XML Cite \textit{L. von Wolfersdorf}, Z. Anal. Anwend. 10, No. 2, 193--200 (1991; Zbl 0764.35050) Full Text: DOI
Bluman, G. W.; Kumei, S. Symmetry-based algorithms to relate partial differential equations. II: Linearization by nonlocal symmetries. (English) Zbl 0718.35004 Eur. J. Appl. Math. 1, No. 3, 217-223 (1990). Reviewer: G.W.Bluman MSC: 35A30 35G20 35K55 PDF BibTeX XML Cite \textit{G. W. Bluman} and \textit{S. Kumei}, Eur. J. Appl. Math. 1, No. 3, 217--223 (1990; Zbl 0718.35004) Full Text: DOI
von Wolfersdorf, Lothar On the linearization of the Satsuma-Mimura diffusion equation. (English) Zbl 0739.35078 Math. Nachr. 145, 243-254 (1990). Reviewer: A.Kirsch (Erlangen) MSC: 35Q35 35K55 PDF BibTeX XML Cite \textit{L. von Wolfersdorf}, Math. Nachr. 145, 243--254 (1990; Zbl 0739.35078) Full Text: DOI
Vorus, W. S. The solution of Burgers’ equation for sinusoidal excitation at the upstream boundary. (English) Zbl 0702.76102 J. Eng. Math. 23, No. 3, 219-237 (1989). MSC: 76R50 76N15 PDF BibTeX XML Cite \textit{W. S. Vorus}, J. Eng. Math. 23, No. 3, 219--237 (1989; Zbl 0702.76102) Full Text: DOI
Nariboli, G. A. Bäcklund transformation of a “variable viscosity” Burgers equation. (English) Zbl 0695.35185 Int. J. Eng. Sci. 26, No. 3, 249-252 (1988). MSC: 35Q99 58J72 35B20 PDF BibTeX XML Cite \textit{G. A. Nariboli}, Int. J. Eng. Sci. 26, No. 3, 249--252 (1988; Zbl 0695.35185) Full Text: DOI
Imbrie, John Z. Directed polymers in a random environment. (English) Zbl 0641.60084 Mathematical quantum field theory and related topics, Proc. Conf., Montreal/Can. 1987, CMS Conf. Proc. 9, 83-90 (1988). Reviewer: Yang Weizhe MSC: 60J60 82D30 PDF BibTeX XML
Greenberg, J. M. Integrable transport processes. (English) Zbl 0641.35057 Nonlinear hyperbolic problems, Proc. Adv. Res. Workshop, St. Etienne/France 1986, Lect. Notes Math. 1270, 324-341 (1987). MSC: 35Q99 PDF BibTeX XML
Sachdev, P. L. Nonlinear diffusive waves. (English) Zbl 0624.35002 Cambridge etc.: Cambridge University Press. VII, 246 p.; £30.00; $ 49.50 (1987). Reviewer: H.-D.Alber MSC: 35-02 35K55 35K57 35B40 35B20 35Q99 35A30 PDF BibTeX XML
Greenberg, James M.; Alt, Wolfgang Stability results for a diffusion equation with functional drift approximating a chemotaxis model. (English) Zbl 0622.35034 Trans. Am. Math. Soc. 300, 235-258 (1987). Reviewer: P.de Mottoni MSC: 35K55 35L67 35R15 92Exx PDF BibTeX XML Cite \textit{J. M. Greenberg} and \textit{W. Alt}, Trans. Am. Math. Soc. 300, 235--258 (1987; Zbl 0622.35034) Full Text: DOI
Beneš, V. E. Using Hopf-Cole, gauge, and Girsanov transformations to reduce stochastic control problems to Gaussian integrations. (English) Zbl 0617.93075 Theory and applications of nonlinear control systems, Sel. Pap. 7th Int. Symp. Math. Theory Networks Syst., Stockholm 1985, 535-553 (1986). MSC: 93E20 93B17 93C10 60J60 49L20 PDF BibTeX XML
Haberman, Richard Note on the initial formation of shocks. (English) Zbl 0604.35053 SIAM J. Appl. Math. 46, 16-19 (1986). Reviewer: R.Salvi MSC: 35L67 35B25 76L05 PDF BibTeX XML Cite \textit{R. Haberman}, SIAM J. Appl. Math. 46, 16--19 (1986; Zbl 0604.35053) Full Text: DOI
Gutkin, Eugene Propagation of chaos and the Hopf-Cole transformation. (English) Zbl 0606.35041 Adv. Appl. Math. 6, 413-421 (1985). Reviewer: P.Theocaris MSC: 35K55 35A30 37D45 35Q99 PDF BibTeX XML Cite \textit{E. Gutkin}, Adv. Appl. Math. 6, 413--421 (1985; Zbl 0606.35041) Full Text: DOI
Gutkin, E.; Kac, M. Propagation of chaos and the Burgers equation. (English) Zbl 0554.35104 SIAM J. Appl. Math. 43, 971-980 (1983). Reviewer: O.Liess MSC: 35Q99 35B32 PDF BibTeX XML Cite \textit{E. Gutkin} and \textit{M. Kac}, SIAM J. Appl. Math. 43, 971--980 (1983; Zbl 0554.35104) Full Text: DOI
Bitsadze, A. V. A new class of exact solutions of Yang’s equations for SU(2) gauge fields. (English. Russian original) Zbl 0542.35075 Sov. Math., Dokl. 27, 396-399 (1983); translation from Dokl. Akad. Nauk SSSR 269, 781-784 (1983). Reviewer: E.Kalnins MSC: 35Q99 81T08 PDF BibTeX XML Cite \textit{A. V. Bitsadze}, Sov. Math., Dokl. 27, 396--399 (1983; Zbl 0542.35075); translation from Dokl. Akad. Nauk SSSR 269, 781--784 (1983)
Lax, Peter D. Singular perturbation of partial differential equations of mathematical physics. (English) Zbl 0527.35068 Differential geometry and differential equations, Proc. 1980 Beijing Sympos., Vol. 2, 711-716 (1982). MSC: 35Q99 35B25 35B40 PDF BibTeX XML
Parker, D. F. The decay of sawtooth solutions to the Burgers equation. (English) Zbl 0427.35062 Proc. R. Soc. Lond., Ser. A 369, 409-424 (1980). MSC: 35Q99 35K60 76Q05 35C05 35B10 PDF BibTeX XML Cite \textit{D. F. Parker}, Proc. R. Soc. Lond., Ser. A 369, 409--424 (1980; Zbl 0427.35062) Full Text: DOI