Chen, Rong; Yang, Zhichun; Zhou, Shouming Existence and uniqueness of the global conservative weak solutions for a cubic Camassa-Holm type equation. (English) Zbl 07801721 J. Differ. Equations 386, 480-518 (2024). MSC: 35D30 35A02 35G25 35Q35 PDFBibTeX XMLCite \textit{R. Chen} et al., J. Differ. Equations 386, 480--518 (2024; Zbl 07801721) Full Text: DOI
Ming, Sen; Du, Jiayi; Ma, Yaxian; Su, Yeqin Formation of singularity of solution to a nonlinear shallow water equation. (English) Zbl 07772814 J. Inequal. Appl. 2023, Paper No. 37, 15 p. (2023). MSC: 35Q35 35B44 76B15 PDFBibTeX XMLCite \textit{S. Ming} et al., J. Inequal. Appl. 2023, Paper No. 37, 15 p. (2023; Zbl 07772814) Full Text: DOI
Chen, Robin Ming; Hu, Tianqiao; Liu, Yue The shallow-water models with cubic nonlinearity. (English) Zbl 1490.35303 J. Math. Fluid Mech. 24, No. 2, Paper No. 49, 31 p. (2022). MSC: 35Q35 35Q31 76B15 35C20 35B40 35B44 35G25 PDFBibTeX XMLCite \textit{R. M. Chen} et al., J. Math. Fluid Mech. 24, No. 2, Paper No. 49, 31 p. (2022; Zbl 1490.35303) Full Text: DOI
Anco, Stephen; He, Huijun; Qiao, Zhijun Local well-posedness and blow-up for a family of \(U(1)\)-invariant peakon equations. (English) Zbl 1455.35056 J. Differ. Equations 275, 757-789 (2021). MSC: 35G25 35B44 35Q55 PDFBibTeX XMLCite \textit{S. Anco} et al., J. Differ. Equations 275, 757--789 (2021; Zbl 1455.35056) Full Text: DOI arXiv
Zhang, Lei; Qiao, Zhijun Global-in-time solvability and blow-up for a non-isospectral two-component cubic Camassa-Holm system in a critical Besov space. (English) Zbl 1458.35125 J. Differ. Equations 274, 414-460 (2021). Reviewer: Giuseppe Maria Coclite (Bari) MSC: 35D35 35G50 35B44 PDFBibTeX XMLCite \textit{L. Zhang} and \textit{Z. Qiao}, J. Differ. Equations 274, 414--460 (2021; Zbl 1458.35125) Full Text: DOI arXiv
Wu, Yemo; Xu, Xiurong; Zuo, Dafeng Integrable systems, multicomponent twisted Heisenberg-Virasoro algebra and its central extensions. (English) Zbl 1472.35281 Front. Math. China 15, No. 6, 1231-1243 (2020). MSC: 35Q31 17B68 32M10 37K10 76B15 PDFBibTeX XMLCite \textit{Y. Wu} et al., Front. Math. China 15, No. 6, 1231--1243 (2020; Zbl 1472.35281) Full Text: DOI
Cherifi Hadjiat, Amina; Lansari, Azzeddine Surjectivity of certain adjoint operators and applications. (English) Zbl 1483.17016 Arab. J. Math. 9, No. 3, 567-588 (2020). Reviewer: Anatoliy Petravchuk (Kyiv) MSC: 17B66 57R25 PDFBibTeX XMLCite \textit{A. Cherifi Hadjiat} and \textit{A. Lansari}, Arab. J. Math. 9, No. 3, 567--588 (2020; Zbl 1483.17016) Full Text: DOI
Zhang, Lei; Qiao, Zhijun The periodic Cauchy problem for a two-component non-isospectral cubic Camassa-Holm system. (English) Zbl 1428.35101 J. Differ. Equations 268, No. 3, 1270-1305 (2020). MSC: 35G25 35B10 35B44 37K10 PDFBibTeX XMLCite \textit{L. Zhang} and \textit{Z. Qiao}, J. Differ. Equations 268, No. 3, 1270--1305 (2020; Zbl 1428.35101) Full Text: DOI
Zuo, Dafeng Supersymmetric Euler equations associated to the \(N \leq 3\) Neveu-Schwarz algebra. (English) Zbl 1472.37063 J. Math. Phys. 60, No. 12, 123505, 11 p. (2019). MSC: 37J37 17B65 17B80 PDFBibTeX XMLCite \textit{D. Zuo}, J. Math. Phys. 60, No. 12, 123505, 11 p. (2019; Zbl 1472.37063) Full Text: DOI
Zhang, Lei Non-uniform dependence and well-posedness for the rotation-Camassa-Holm equation on the torus. (English) Zbl 1433.35312 J. Differ. Equations 267, No. 9, 5049-5083 (2019). MSC: 35Q35 35Q86 76U60 76B15 76B03 86A05 PDFBibTeX XMLCite \textit{L. Zhang}, J. Differ. Equations 267, No. 9, 5049--5083 (2019; Zbl 1433.35312) Full Text: DOI
Guan, Chunxia; Zhu, Hao Well-posedness of a class of solutions to an integrable two-component Camassa-Holm system. (English) Zbl 1406.35100 J. Math. Anal. Appl. 470, No. 1, 413-433 (2019). MSC: 35G55 PDFBibTeX XMLCite \textit{C. Guan} and \textit{H. Zhu}, J. Math. Anal. Appl. 470, No. 1, 413--433 (2019; Zbl 1406.35100) Full Text: DOI
Ge, Yanyan; Zuo, Dafeng A new class of Euler equation on the dual of the \(N=1\) extended Neveu-Schwarz algebra. (English) Zbl 1403.37074 J. Math. Phys. 59, No. 11, 113505, 8 p. (2018). MSC: 37K10 35Q31 17A70 81Q60 76B15 PDFBibTeX XMLCite \textit{Y. Ge} and \textit{D. Zuo}, J. Math. Phys. 59, No. 11, 113505, 8 p. (2018; Zbl 1403.37074) Full Text: DOI
Lee, Jae Min; Preston, Stephen C. Local well-posedness of the Camassa-Holm equation on the real line. (English) Zbl 1361.35147 Discrete Contin. Dyn. Syst. 37, No. 6, 3285-3299 (2017). MSC: 35Q35 53D25 76B15 37K65 PDFBibTeX XMLCite \textit{J. M. Lee} and \textit{S. C. Preston}, Discrete Contin. Dyn. Syst. 37, No. 6, 3285--3299 (2017; Zbl 1361.35147) Full Text: DOI arXiv
Yan, Wei; Li, Yongsheng The Cauchy problem for the modified two-component Camassa-Holm system in critical Besov space. (English) Zbl 1336.35121 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 32, No. 2, 443-469 (2015). Reviewer: David Ambrose (Philadelphia) MSC: 35G25 35Q53 35A01 PDFBibTeX XMLCite \textit{W. Yan} and \textit{Y. Li}, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 32, No. 2, 443--469 (2015; Zbl 1336.35121) Full Text: DOI
Li, Hongmin; Li, Yuqi; Chen, Yong Bi-Hamiltonian structure of multi-component Novikov equation. (English) Zbl 1420.37074 J. Nonlinear Math. Phys. 21, No. 4, 509-520 (2014). MSC: 37K10 35Q51 35Q53 PDFBibTeX XMLCite \textit{H. Li} et al., J. Nonlinear Math. Phys. 21, No. 4, 509--520 (2014; Zbl 1420.37074) Full Text: DOI
Zuo, Dafeng The Frobenius-Virasoro algebra and Euler equations. (English) Zbl 1304.35627 J. Geom. Phys. 86, 203-210 (2014). MSC: 35Q53 17B68 35Q31 PDFBibTeX XMLCite \textit{D. Zuo}, J. Geom. Phys. 86, 203--210 (2014; Zbl 1304.35627) Full Text: DOI arXiv
Brandolese, Lorenzo; Cortez, Manuel Fernando On permanent and breaking waves in hyperelastic rods and rings. (English) Zbl 1295.35009 J. Funct. Anal. 266, No. 12, 6954-6987 (2014). MSC: 35A02 35B60 35B44 74K10 PDFBibTeX XMLCite \textit{L. Brandolese} and \textit{M. F. Cortez}, J. Funct. Anal. 266, No. 12, 6954--6987 (2014; Zbl 1295.35009) Full Text: DOI arXiv
Zong, Xiju; Sun, Shurong On the global attractor of the two-component \(\pi\)-Camassa-Holm equation with viscous terms. (English) Zbl 1302.35070 Nonlinear Anal., Real World Appl. 20, 82-98 (2014). MSC: 35B41 35Q35 PDFBibTeX XMLCite \textit{X. Zong} and \textit{S. Sun}, Nonlinear Anal., Real World Appl. 20, 82--98 (2014; Zbl 1302.35070) Full Text: DOI
Zong, Xiju On the global boundary stabilization of the Camassa-Holm equation. (English) Zbl 1295.35110 Nonlinear Anal., Real World Appl. 15, 221-228 (2014). MSC: 35B40 93C20 35Q35 PDFBibTeX XMLCite \textit{X. Zong}, Nonlinear Anal., Real World Appl. 15, 221--228 (2014; Zbl 1295.35110) Full Text: DOI
Brandolese, Lorenzo; Cortez, Manuel Fernando Blowup issues for a class of nonlinear dispersive wave equations. (English) Zbl 1293.35053 J. Differ. Equations 256, No. 12, 3981-3998 (2014). MSC: 35B44 35G25 PDFBibTeX XMLCite \textit{L. Brandolese} and \textit{M. F. Cortez}, J. Differ. Equations 256, No. 12, 3981--3998 (2014; Zbl 1293.35053) Full Text: DOI arXiv
Cao, Hai-Yan; Sun, Zhi-Zhong; Gao, Guang-Hua A three-level linearized finite difference scheme for the Camassa-Holm equation. (English) Zbl 1290.65071 Numer. Methods Partial Differ. Equations 30, No. 2, 451-471 (2014). Reviewer: Vit Dolejsi (Praha) MSC: 65M06 35Q35 65M12 PDFBibTeX XMLCite \textit{H.-Y. Cao} et al., Numer. Methods Partial Differ. Equations 30, No. 2, 451--471 (2014; Zbl 1290.65071) Full Text: DOI
Lv, Guangying; Wang, Xiaohuan Hölder continuity on \({\mu}\)-\(b\) equation. (English) Zbl 1284.35136 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 102, 30-35 (2014). MSC: 35G25 35B30 35L05 PDFBibTeX XMLCite \textit{G. Lv} and \textit{X. Wang}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 102, 30--35 (2014; Zbl 1284.35136) Full Text: DOI
Li, Nianhua; Liu, Q. P. Bi-Hamiltonian structure of a three-component Camassa-Holm type equation. (English) Zbl 1420.37076 J. Nonlinear Math. Phys. 20, No. 1, 126-134 (2013). MSC: 37K10 35Q51 PDFBibTeX XMLCite \textit{N. Li} and \textit{Q. P. Liu}, J. Nonlinear Math. Phys. 20, No. 1, 126--134 (2013; Zbl 1420.37076) Full Text: DOI
Guan, Chunxia; Yin, Zhaoyang On the existence of global weak solutions to an integrable two-component Camassa-Holm shallow-water system. (English) Zbl 1288.35196 Proc. Edinb. Math. Soc., II. Ser. 56, No. 3, 755-775 (2013). Reviewer: David Ambrose (Philadelphia) MSC: 35G25 35Q53 35Q35 PDFBibTeX XMLCite \textit{C. Guan} and \textit{Z. Yin}, Proc. Edinb. Math. Soc., II. Ser. 56, No. 3, 755--775 (2013; Zbl 1288.35196) Full Text: DOI Link
Tan, Wenke; Liu, Yue; Yin, Zhaoyang On the global weak solution to a generalized two-component Camassa-Holm system. (English) Zbl 1308.35060 Q. Appl. Math. 71, No. 4, 661-677 (2013). MSC: 35D30 35G25 35A01 35Q35 PDFBibTeX XMLCite \textit{W. Tan} et al., Q. Appl. Math. 71, No. 4, 661--677 (2013; Zbl 1308.35060) Full Text: DOI
Zhu, Mingxuan; Jin, Liangbing; Jiang, Zaihong A new blow-up criterion for the DGH equation. (English) Zbl 1242.35198 Abstr. Appl. Anal. 2012, Article ID 515948, 10 p. (2012). MSC: 35Q53 PDFBibTeX XMLCite \textit{M. Zhu} et al., Abstr. Appl. Anal. 2012, Article ID 515948, 10 p. (2012; Zbl 1242.35198) Full Text: DOI
Liu, Jingjing; Yin, Zhaoyang On the Cauchy problem of a periodic 2-component \(\mu\)-Hunter-Saxton system. (English) Zbl 1228.35093 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 75, No. 1, 131-142 (2012). MSC: 35G25 35B44 35Q53 PDFBibTeX XMLCite \textit{J. Liu} and \textit{Z. Yin}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 75, No. 1, 131--142 (2012; Zbl 1228.35093) Full Text: DOI arXiv
Zhang, Ling; Zuo, Dafeng Integrable hierarchies related to the Kuper-CH spectral problem. (English) Zbl 1317.37083 J. Math. Phys. 52, No. 7, 073503, 11 p. (2011). MSC: 37K10 37K25 35P30 81Q60 PDFBibTeX XMLCite \textit{L. Zhang} and \textit{D. Zuo}, J. Math. Phys. 52, No. 7, 073503, 11 p. (2011; Zbl 1317.37083) Full Text: DOI
Zong, Xiju; Cheng, Xingong; Wang, Zhonghua; Han, Zhenlai Initial boundary value problem and asymptotic stabilization of the two-component Camassa-Holm equation. (English) Zbl 1228.35212 Abstr. Appl. Anal. 2011, Article ID 635851, 20 p. (2011). MSC: 35Q53 35Q35 76B15 35B35 PDFBibTeX XMLCite \textit{X. Zong} et al., Abstr. Appl. Anal. 2011, Article ID 635851, 20 p. (2011; Zbl 1228.35212) Full Text: DOI
Guan, Chunxia; Yin, Zhaoyang Global weak solutions for a two-component Camassa-Holm shallow water system. (English) Zbl 1210.35209 J. Funct. Anal. 260, No. 4, 1132-1154 (2011). MSC: 35Q53 35Q35 76B15 76B03 PDFBibTeX XMLCite \textit{C. Guan} and \textit{Z. Yin}, J. Funct. Anal. 260, No. 4, 1132--1154 (2011; Zbl 1210.35209) Full Text: DOI
Cho, Chien-Hong; Wunsch, Marcus Global and singular solutions to the generalized Proudman-Johnson equation. (English) Zbl 1204.35067 J. Differ. Equations 249, No. 2, 392-413 (2010). MSC: 35D30 74H35 35Q35 35B44 PDFBibTeX XMLCite \textit{C.-H. Cho} and \textit{M. Wunsch}, J. Differ. Equations 249, No. 2, 392--413 (2010; Zbl 1204.35067) Full Text: DOI
Guan, Chunxia; Yin, Zhaoyang Global existence and blow-up phenomena for an integrable two-component Camassa-Holm shallow water system. (English) Zbl 1190.35039 J. Differ. Equations 248, No. 8, 2003-2014 (2010). MSC: 35B44 35G25 35Q35 PDFBibTeX XMLCite \textit{C. Guan} and \textit{Z. Yin}, J. Differ. Equations 248, No. 8, 2003--2014 (2010; Zbl 1190.35039) Full Text: DOI
Mustafa, Octavian G. On smooth traveling waves of an integrable two-component Camassa-Holm shallow water system. (English) Zbl 1231.76063 Wave Motion 46, No. 6, 397-402 (2009). MSC: 76B25 35Q35 PDFBibTeX XMLCite \textit{O. G. Mustafa}, Wave Motion 46, No. 6, 397--402 (2009; Zbl 1231.76063) Full Text: DOI
Hu, Qiaoyi; Yin, Zhaoyang Blowup and blowup rate of solutions to a weakly dissipative periodic rod equation. (English) Zbl 1298.35174 J. Math. Phys. 50, No. 8, 083503, 16 p. (2009). MSC: 35Q53 35B10 35B44 74H35 74K10 PDFBibTeX XMLCite \textit{Q. Hu} and \textit{Z. Yin}, J. Math. Phys. 50, No. 8, 083503, 16 p. (2009; Zbl 1298.35174) Full Text: DOI
Christov, Ognyan; Hakkaev, Sevdzhan On the Cauchy problem for the periodic \(b\)-family of equations and of the non-uniform continuity of Degasperis-Procesi equation. (English) Zbl 1178.35081 J. Math. Anal. Appl. 360, No. 1, 47-56 (2009). Reviewer: Lokenath Debnath (Edinburg) MSC: 35B44 35Q35 35C07 PDFBibTeX XMLCite \textit{O. Christov} and \textit{S. Hakkaev}, J. Math. Anal. Appl. 360, No. 1, 47--56 (2009; Zbl 1178.35081) Full Text: DOI
Kolev, Boris Geometric differences between the Burgers and the Camassa-Holm equations. (English) Zbl 1362.35222 J. Nonlinear Math. Phys. 15, Suppl. 2, 116-132 (2008). MSC: 35Q31 76B10 76B15 PDFBibTeX XMLCite \textit{B. Kolev}, J. Nonlinear Math. Phys. 15, 116--132 (2008; Zbl 1362.35222) Full Text: DOI
Guha, Partha Geodesic flow in extended Bott-Virasoro group and generalized two-component Peakon type dual systems. (English) Zbl 1157.35483 Rev. Math. Phys. 20, No. 10, 1191-1208 (2008). MSC: 35Q58 35Q51 37K10 37K30 53A07 53B50 53C22 PDFBibTeX XMLCite \textit{P. Guha}, Rev. Math. Phys. 20, No. 10, 1191--1208 (2008; Zbl 1157.35483) Full Text: DOI