Dougalis, Vassilios A.; Duran, Angel; Saridaki, Leetha On the numerical approximation of Boussinesq/Boussinesq systems for internal waves. (English) Zbl 07777374 Numer. Methods Partial Differ. Equations 39, No. 5, 3677-3704 (2023). MSC: 65M60 65M06 65N30 65L06 35C08 35A01 35A02 76B03 35Q31 PDFBibTeX XMLCite \textit{V. A. Dougalis} et al., Numer. Methods Partial Differ. Equations 39, No. 5, 3677--3704 (2023; Zbl 07777374) Full Text: DOI
Landoulsi, Oussama; Roudenko, Svetlana; Yang, Kai Interaction with an obstacle in the 2D focusing nonlinear Schrödinger equation. (English) Zbl 1527.35383 Adv. Comput. Math. 49, No. 5, Paper No. 71, 44 p. (2023). MSC: 35Q55 35Q41 58J32 58J37 65N06 65M06 35B40 35C08 35C07 35B44 35A01 35A23 35R09 PDFBibTeX XMLCite \textit{O. Landoulsi} et al., Adv. Comput. Math. 49, No. 5, Paper No. 71, 44 p. (2023; Zbl 1527.35383) Full Text: DOI arXiv
Yang, Kai High order conservative schemes for the generalized Benjamin-Ono equation on the unbounded domain. (English) Zbl 07708336 J. Sci. Comput. 96, No. 2, Paper No. 35, 27 p. (2023). MSC: 35Q53 35L65 65M70 65M06 65L06 65N35 44A15 PDFBibTeX XMLCite \textit{K. Yang}, J. Sci. Comput. 96, No. 2, Paper No. 35, 27 p. (2023; Zbl 07708336) Full Text: DOI arXiv
Liu, Wei; Yuan, Yongjun; Zhao, Xiaofei Computing the action ground state for the rotating nonlinear Schrödinger equation. (English) Zbl 1514.35129 SIAM J. Sci. Comput. 45, No. 2, A397-A426 (2023). MSC: 35J10 35Q55 65N12 PDFBibTeX XMLCite \textit{W. Liu} et al., SIAM J. Sci. Comput. 45, No. 2, A397--A426 (2023; Zbl 1514.35129) Full Text: DOI arXiv
Chakravarty, Sarbarish; Zowada, Michael Multi-lump wave patterns of KPI via integer partitions. (English) Zbl 1512.65237 Physica D 446, Article ID 133644, 18 p. (2023). Reviewer: Yinhua Xia (Hefei) MSC: 65M99 65H04 35B36 35C08 37K35 37K10 34M55 76L05 35Q53 35Q35 PDFBibTeX XMLCite \textit{S. Chakravarty} and \textit{M. Zowada}, Physica D 446, Article ID 133644, 18 p. (2023; Zbl 1512.65237) Full Text: DOI
Flamarion, Marcelo V.; Pelinovsky, Efim Soliton interactions with an external forcing: the modified Korteweg-de Vries framework. (English) Zbl 1508.35119 Chaos Solitons Fractals 165, Part 2, Article ID 112889, 7 p. (2022). MSC: 35Q53 65M70 35C08 PDFBibTeX XMLCite \textit{M. V. Flamarion} and \textit{E. Pelinovsky}, Chaos Solitons Fractals 165, Part 2, Article ID 112889, 7 p. (2022; Zbl 1508.35119) Full Text: DOI arXiv
Dougalis, Vassilios A.; Duran, Angel; Saridaki, Leetha On some Boussinesq/full dispersion systems for internal waves: numerical solution and solitary waves. (English) Zbl 1493.65167 Water Waves 4, No. 2, 193-237 (2022). MSC: 65M70 76B15 76B25 PDFBibTeX XMLCite \textit{V. A. Dougalis} et al., Water Waves 4, No. 2, 193--237 (2022; Zbl 1493.65167) Full Text: DOI arXiv
Wang, Fuzhang; Hou, Enran; Salama, Samir A.; Khater, Mostafa M. A. Numerical investigation of the nonlinear fractional Ostrovsky equation. (English) Zbl 1504.35388 Fractals 30, No. 5, Article ID 2240142, 9 p. (2022). MSC: 35Q35 76B15 76F10 76F65 76X05 78A60 82D10 35C08 35C07 65D07 65N99 26A33 35R11 35R10 PDFBibTeX XMLCite \textit{F. Wang} et al., Fractals 30, No. 5, Article ID 2240142, 9 p. (2022; Zbl 1504.35388) Full Text: DOI
Dougalis, V.; Duran, A.; Saridaki, L. Numerical solution of internal-wave systems in the intermediate long wave and the Benjamin-Ono regimes. (English) Zbl 1492.65279 Bull. Hell. Math. Soc. 66, 11-25 (2022). MSC: 65M70 76B25 65M15 PDFBibTeX XMLCite \textit{V. Dougalis} et al., Bull. Hell. Math. Soc. 66, 11--25 (2022; Zbl 1492.65279) Full Text: arXiv Link
Ghanadian, F.; Pourgholi, R.; Tabasi, S. H. Numerical approximation for inverse problem of the Ostrovsky-Burgers equation. (English) Zbl 1482.65172 Iran. J. Numer. Anal. Optim. 12, No. 1, 73-109 (2022). MSC: 65M32 35Q53 35B35 65M70 65M12 PDFBibTeX XMLCite \textit{F. Ghanadian} et al., Iran. J. Numer. Anal. Optim. 12, No. 1, 73--109 (2022; Zbl 1482.65172) Full Text: DOI
Roudenko, Svetlana; Wang, Zhongming; Yang, Kai Dynamics of solutions in the generalized Benjamin-Ono equation: a numerical study. (English) Zbl 07515841 J. Comput. Phys. 445, Article ID 110570, 25 p. (2021). MSC: 35Qxx 76Bxx 65Mxx PDFBibTeX XMLCite \textit{S. Roudenko} et al., J. Comput. Phys. 445, Article ID 110570, 25 p. (2021; Zbl 07515841) Full Text: DOI arXiv
Dougalis, Vassilios A.; Durán, Angel; Saridaki, Leetha On solitary-wave solutions of Boussinesq/Boussinesq systems for internal waves. (English) Zbl 1508.35068 Physica D 428, Article ID 133051, 23 p. (2021). MSC: 35Q35 76B25 35C08 35A24 35A01 65L12 65L06 PDFBibTeX XMLCite \textit{V. A. Dougalis} et al., Physica D 428, Article ID 133051, 23 p. (2021; Zbl 1508.35068) Full Text: DOI arXiv
Bona, Jerry L.; Durán, Angel; Mitsotakis, Dimitrios Solitary-wave solutions of Benjamin-Ono and other systems for internal waves. I: Approximations. (English) Zbl 1460.76146 Discrete Contin. Dyn. Syst. 41, No. 1, 87-111 (2021). MSC: 76B55 76B25 76M22 65M70 PDFBibTeX XMLCite \textit{J. L. Bona} et al., Discrete Contin. Dyn. Syst. 41, No. 1, 87--111 (2021; Zbl 1460.76146) Full Text: DOI
Erbay, H. A.; Erbay, S.; Erkip, A. Numerical computation of solitary wave solutions of the Rosenau equation. (English) Zbl 1524.35524 Wave Motion 98, Article ID 102618, 10 p. (2020). MSC: 35Q53 35C08 65M99 74J35 74S99 PDFBibTeX XMLCite \textit{H. A. Erbay} et al., Wave Motion 98, Article ID 102618, 10 p. (2020; Zbl 1524.35524) Full Text: DOI arXiv
Katsaounis, Theodoros; Mitsotakis, Dimitrios; Sadaka, Georges Boussinesq-Peregrine water wave models and their numerical approximation. (English) Zbl 1437.76022 J. Comput. Phys. 417, Article ID 109579, 23 p. (2020). MSC: 76M10 65M60 76B15 PDFBibTeX XMLCite \textit{T. Katsaounis} et al., J. Comput. Phys. 417, Article ID 109579, 23 p. (2020; Zbl 1437.76022) Full Text: DOI arXiv
Zhang, Qian; Xia, Yinhua Discontinuous Galerkin methods for the Ostrovsky-Vakhnenko equation. (English) Zbl 1448.35460 J. Sci. Comput. 82, No. 2, Paper No. 24, 26 p. (2020). MSC: 35Q53 65M60 35C08 PDFBibTeX XMLCite \textit{Q. Zhang} and \textit{Y. Xia}, J. Sci. Comput. 82, No. 2, Paper No. 24, 26 p. (2020; Zbl 1448.35460) Full Text: DOI arXiv
Ridder, J.; Ruf, A. M. A convergent finite difference scheme for the Ostrovsky-Hunter equation with Dirichlet boundary conditions. (English) Zbl 1433.65165 BIT 59, No. 3, 775-796 (2019). Reviewer: Kanakadurga Sivakumar (Chennai) MSC: 65M06 35M33 35L35 35Q35 65M12 76U60 86A05 PDFBibTeX XMLCite \textit{J. Ridder} and \textit{A. M. Ruf}, BIT 59, No. 3, 775--796 (2019; Zbl 1433.65165) Full Text: DOI arXiv
Le, Uyen; Pelinovsky, Dmitry E. Convergence of Petviashvili’s method near periodic waves in the fractional Korteweg-de Vries equation. (English) Zbl 1419.35178 SIAM J. Math. Anal. 51, No. 4, 2850-2883 (2019). MSC: 35Q53 35P30 37K50 37K55 65J15 PDFBibTeX XMLCite \textit{U. Le} and \textit{D. E. Pelinovsky}, SIAM J. Math. Anal. 51, No. 4, 2850--2883 (2019; Zbl 1419.35178) Full Text: DOI arXiv
Liu, Bin; Li, Lu; Malomed, Boris A. Stability band structure for periodic states in periodic potentials. (English) Zbl 1420.35367 Appl. Numer. Math. 141, 44-53 (2019). MSC: 35Q55 78A50 78A60 35B35 65N25 65N06 PDFBibTeX XMLCite \textit{B. Liu} et al., Appl. Numer. Math. 141, 44--53 (2019; Zbl 1420.35367) Full Text: DOI arXiv
Sato, Shun Stability and convergence of a conservative finite difference scheme for the modified Hunter-Saxton equation. (English) Zbl 1416.65282 BIT 59, No. 1, 213-241 (2019). Reviewer: Marius Ghergu (Dublin) MSC: 65M06 65M12 35Q35 76B15 76B45 PDFBibTeX XMLCite \textit{S. Sato}, BIT 59, No. 1, 213--241 (2019; Zbl 1416.65282) Full Text: DOI arXiv
Durán, A. An efficient method to compute solitary wave solutions of fractional Korteweg-de Vries equations. (English) Zbl 1499.65185 Int. J. Comput. Math. 95, No. 6-7, 1362-1374 (2018). MSC: 65H10 65M70 65Z05 PDFBibTeX XMLCite \textit{A. Durán}, Int. J. Comput. Math. 95, No. 6--7, 1362--1374 (2018; Zbl 1499.65185) Full Text: DOI arXiv
Chiron, David; Scheid, Claire Multiple branches of travelling waves for the Gross-Pitaevskii equation. (English) Zbl 1393.35216 Nonlinearity 31, No. 6, 2809-2853 (2018). MSC: 35Q55 35B38 35C07 35J61 35Q40 35Q53 35C08 65M06 65F15 65H10 PDFBibTeX XMLCite \textit{D. Chiron} and \textit{C. Scheid}, Nonlinearity 31, No. 6, 2809--2853 (2018; Zbl 1393.35216) Full Text: DOI
Clarke, S.; Gorshkov, K.; Grimshaw, R.; Stepanyants, Y. Decay of Kadomtsev-Petviashvili lumps in dissipative media. (English) Zbl 1381.35010 Physica D 366, 43-50 (2018). MSC: 35C08 35Q53 65Z05 PDFBibTeX XMLCite \textit{S. Clarke} et al., Physica D 366, 43--50 (2018; Zbl 1381.35010) Full Text: DOI arXiv
Muslu, Gulcin M.; Borluk, Handan Numerical solution for a general class of nonlocal nonlinear wave equations arising in elasticity. (English) Zbl 07776769 ZAMM, Z. Angew. Math. Mech. 97, No. 12, 1600-1610 (2017). MSC: 65M70 35C07 PDFBibTeX XMLCite \textit{G. M. Muslu} and \textit{H. Borluk}, ZAMM, Z. Angew. Math. Mech. 97, No. 12, 1600--1610 (2017; Zbl 07776769) Full Text: DOI arXiv
Coclite, G. M.; Ridder, J.; Risebro, N. H. A convergent finite difference scheme for the Ostrovsky-Hunter equation on a bounded domain. (English) Zbl 1368.65133 BIT 57, No. 1, 93-122 (2017). Reviewer: Charis Harley (Johannesburg) MSC: 65M06 35M33 35L35 65M12 PDFBibTeX XMLCite \textit{G. M. Coclite} et al., BIT 57, No. 1, 93--122 (2017; Zbl 1368.65133) Full Text: DOI
Álvarez, J.; Durán, A. Petviashvili type methods for traveling wave computations. II: Acceleration with vector extrapolation methods. (English) Zbl 07313629 Math. Comput. Simul. 123, 19-36 (2016). MSC: 65-XX 78-XX PDFBibTeX XMLCite \textit{J. Álvarez} and \textit{A. Durán}, Math. Comput. Simul. 123, 19--36 (2016; Zbl 07313629) Full Text: DOI arXiv Link
Ablowitz, Mark J.; Demirci, Ali; Ma, Yi-Ping Dispersive shock waves in the Kadomtsev-Petviashvili and two dimensional Benjamin-Ono equations. (English) Zbl 1415.35237 Physica D 333, 84-98 (2016). MSC: 35Q53 76L05 65M99 PDFBibTeX XMLCite \textit{M. J. Ablowitz} et al., Physica D 333, 84--98 (2016; Zbl 1415.35237) Full Text: DOI arXiv
Soffer, Avy; Zhao, Xiaofei A modulation equations approach for numerically solving the moving soliton and radiation solutions of NLS. (English) Zbl 1364.35341 Physica D 320, 77-88 (2016). MSC: 35Q55 35C08 65L15 65M70 PDFBibTeX XMLCite \textit{A. Soffer} and \textit{X. Zhao}, Physica D 320, 77--88 (2016; Zbl 1364.35341) Full Text: DOI arXiv
Dyachenko, S. A.; Lushnikov, P. M.; Korotkevich, A. O. Branch cuts of Stokes wave on deep water. I: Numerical solution and Padé approximation. (English) Zbl 1356.35166 Stud. Appl. Math. 137, No. 4, 419-472 (2016). MSC: 35Q31 76B07 41A21 76B15 65D20 35B32 35R35 PDFBibTeX XMLCite \textit{S. A. Dyachenko} et al., Stud. Appl. Math. 137, No. 4, 419--472 (2016; Zbl 1356.35166) Full Text: DOI arXiv
Lu, Jianfeng; Ying, Lexing Sparsifying preconditioner for soliton calculations. (English) Zbl 1349.65606 J. Comput. Phys. 315, 458-466 (2016). MSC: 65N25 65F08 35C08 35J91 35Q55 65N22 PDFBibTeX XMLCite \textit{J. Lu} and \textit{L. Ying}, J. Comput. Phys. 315, 458--466 (2016; Zbl 1349.65606) Full Text: DOI arXiv
Nishiyama, Hirota; Noi, Takahiro Conservative difference schemes for the numerical solution of the Gardner equation. (English) Zbl 1339.65134 Comput. Appl. Math. 35, No. 1, 75-95 (2016). MSC: 65M06 35Q53 PDFBibTeX XMLCite \textit{H. Nishiyama} and \textit{T. Noi}, Comput. Appl. Math. 35, No. 1, 75--95 (2016; Zbl 1339.65134) Full Text: DOI
Olson, D.; Shukla, S.; Simpson, G.; Spirn, D. Petviashvilli’s method for the Dirichlet problem. (English) Zbl 1339.65222 J. Sci. Comput. 66, No. 1, 296-320 (2016). Reviewer: Calin Ioan Gheorghiu (Cluj-Napoca) MSC: 65N30 65N12 74J30 74J35 35J61 PDFBibTeX XMLCite \textit{D. Olson} et al., J. Sci. Comput. 66, No. 1, 296--320 (2016; Zbl 1339.65222) Full Text: DOI arXiv
Alonso-Mallo, I.; Reguera, N. Numerical detection and generation of solitary waves for a nonlinear wave equation. (English) Zbl 1454.35317 Wave Motion 56, 137-146 (2015). MSC: 35Q53 35C08 65M60 PDFBibTeX XMLCite \textit{I. Alonso-Mallo} and \textit{N. Reguera}, Wave Motion 56, 137--146 (2015; Zbl 1454.35317) Full Text: DOI
Brugnano, Luigi (ed.); Sergeyev, Yaroslav D. (ed.); Zhigljavsky, Anatoly A. (ed.) Preface to the special issue NUMTA 2013. (English) Zbl 1329.00188 Commun. Nonlinear Sci. Numer. Simul. 21, No. 1-3, 1-2 (2015). MSC: 00B25 65-06 PDFBibTeX XMLCite \textit{L. Brugnano} (ed.) et al., Commun. Nonlinear Sci. Numer. Simul. 21, No. 1--3, 1--2 (2015; Zbl 1329.00188) Full Text: DOI
Álvarez, J.; Durán, Angel An extended Petviashvili method for the numerical generation of traveling and localized waves. (English) Zbl 1457.65035 Commun. Nonlinear Sci. Numer. Simul. 19, No. 7, 2272-2283 (2014). MSC: 65L99 PDFBibTeX XMLCite \textit{J. Álvarez} and \textit{A. Durán}, Commun. Nonlinear Sci. Numer. Simul. 19, No. 7, 2272--2283 (2014; Zbl 1457.65035) Full Text: DOI arXiv
Obregon, M. A.; Sanmiguel-Rojas, E.; Fernandez-Feria, Ramon High accuracy numerical methods for the Gardner-Ostrovsky equation. (English) Zbl 1334.65135 Appl. Math. Comput. 240, 140-148 (2014). MSC: 65M06 37K40 86A05 35Q53 35Q86 76M20 PDFBibTeX XMLCite \textit{M. A. Obregon} et al., Appl. Math. Comput. 240, 140--148 (2014; Zbl 1334.65135) Full Text: DOI
Álvarez, J.; Durán, A. Petviashvili type methods for traveling wave computations. I: Analysis of convergence. (English) Zbl 1293.65079 J. Comput. Appl. Math. 266, 39-51 (2014); corrigendum ibid. 277, 215-216 (2015). MSC: 65H10 35C99 35C07 76B25 PDFBibTeX XMLCite \textit{J. Álvarez} and \textit{A. Durán}, J. Comput. Appl. Math. 266, 39--51 (2014; Zbl 1293.65079) Full Text: DOI arXiv
Clamond, Didier; Dutykh, Denys Fast accurate computation of the fully nonlinear solitary surface gravity waves. (English) Zbl 1290.76018 Comput. Fluids 84, 35-38 (2013). MSC: 76B25 76M25 65T50 PDFBibTeX XMLCite \textit{D. Clamond} and \textit{D. Dutykh}, Comput. Fluids 84, 35--38 (2013; Zbl 1290.76018) Full Text: DOI arXiv
Levandosky, Steven On the stability of solitary waves of a generalized Ostrovsky equation. (English) Zbl 1254.35204 Anal. Math. Phys. 2, No. 4, 407-437 (2012). MSC: 35Q53 35B35 35C08 65M12 PDFBibTeX XMLCite \textit{S. Levandosky}, Anal. Math. Phys. 2, No. 4, 407--437 (2012; Zbl 1254.35204) Full Text: DOI
Simpson, G.; Spiegelman, M. Solitary wave benchmarks in magma dynamics. (English) Zbl 1241.86002 J. Sci. Comput. 49, No. 3, 268-290 (2011). MSC: 86-08 86A17 65N30 PDFBibTeX XMLCite \textit{G. Simpson} and \textit{M. Spiegelman}, J. Sci. Comput. 49, No. 3, 268--290 (2011; Zbl 1241.86002) Full Text: DOI arXiv
Dehghan, Mehdi; Fakhar-Izadi, Farhad The spectral collocation method with three different bases for solving a nonlinear partial differential equation arising in modeling of nonlinear waves. (English) Zbl 1219.65106 Math. Comput. Modelling 53, No. 9-10, 1865-1877 (2011). MSC: 65M70 35Q53 76U05 76M25 PDFBibTeX XMLCite \textit{M. Dehghan} and \textit{F. Fakhar-Izadi}, Math. Comput. Modelling 53, No. 9--10, 1865--1877 (2011; Zbl 1219.65106) Full Text: DOI
Álvarez, J.; Durán, A. A numerical scheme for periodic travelling-wave simulations in some nonlinear dispersive wave models. (English) Zbl 1209.65098 J. Comput. Appl. Math. 235, No. 7, 1790-1797 (2011). MSC: 65M70 35L60 35Q53 76B25 PDFBibTeX XMLCite \textit{J. Álvarez} and \textit{A. Durán}, J. Comput. Appl. Math. 235, No. 7, 1790--1797 (2011; Zbl 1209.65098) Full Text: DOI
Alonso-Mallo, I.; Durán, A.; Reguera, N. Simulation of coherent structures in nonlinear Schrödinger-type equations. (English) Zbl 1220.81077 J. Comput. Phys. 229, No. 21, 8180-8198 (2010). MSC: 81Q05 65M60 PDFBibTeX XMLCite \textit{I. Alonso-Mallo} et al., J. Comput. Phys. 229, No. 21, 8180--8198 (2010; Zbl 1220.81077) Full Text: DOI
Chugunova, Marina; Pelinovsky, Dmitry On the uniform convergence of the Chebyshev interpolants for solitons. (English) Zbl 1185.65186 Math. Comput. Simul. 80, No. 4, 794-803 (2009). Reviewer: Qin Mengzhao (Beijing) MSC: 65M70 35Q51 65D05 65M12 PDFBibTeX XMLCite \textit{M. Chugunova} and \textit{D. Pelinovsky}, Math. Comput. Simul. 80, No. 4, 794--803 (2009; Zbl 1185.65186) Full Text: DOI
Yang, Jianke Newton-conjugate-gradient methods for solitary wave computations. (English) Zbl 1175.65123 J. Comput. Phys. 228, No. 18, 7007-7024 (2009). MSC: 65M70 35Q53 35Q51 35Q55 35Q35 PDFBibTeX XMLCite \textit{J. Yang}, J. Comput. Phys. 228, No. 18, 7007--7024 (2009; Zbl 1175.65123) Full Text: DOI
Yang, Jianke; Lakoba, Taras I. Accelerated imaginary-time evolution methods for the computation of solitary waves. (English) Zbl 1191.35227 Stud. Appl. Math. 120, No. 3, 265-292 (2008). MSC: 35Q51 35J10 35P05 65N22 65Z05 65N12 PDFBibTeX XMLCite \textit{J. Yang} and \textit{T. I. Lakoba}, Stud. Appl. Math. 120, No. 3, 265--292 (2008; Zbl 1191.35227) Full Text: DOI arXiv
Lakoba, T. I.; Yang, J. A mode elimination technique to improve convergence of iteration methods for finding solitary waves. (English) Zbl 1127.65079 J. Comput. Phys. 226, No. 2, 1693-1709 (2007). MSC: 65N06 35J65 PDFBibTeX XMLCite \textit{T. I. Lakoba} and \textit{J. Yang}, J. Comput. Phys. 226, No. 2, 1693--1709 (2007; Zbl 1127.65079) Full Text: DOI arXiv
Lakoba, T. I.; Yang, J. A generalized Petviashvili iteration method for scalar and vector Hamiltonian equations with arbitrary form of nonlinearity. (English) Zbl 1126.35052 J. Comput. Phys. 226, No. 2, 1668-1692 (2007). MSC: 35Q51 37L65 65N99 78A40 PDFBibTeX XMLCite \textit{T. I. Lakoba} and \textit{J. Yang}, J. Comput. Phys. 226, No. 2, 1668--1692 (2007; Zbl 1126.35052) Full Text: DOI arXiv