On the Rosenau equation: Lie symmetries, periodic solutions and solitary wave dynamics
Tài liệu tham khảo
Rosenau, 1988, Dynamics of dense discrete systems: High order effects, Progr. Theoret. Phys., 79, 1028, 10.1143/PTP.79.1028
Park, 1990, On the Rosenau equation, Mat. Apl. Comput., 9, 145
Park, 1992, Pointwise decay estimates of solutions of the generalized Rosenau equation, J. Korean Math. Soc., 29, 261
Park, 1993, On the Rosenau equation in multidimensional space, Nonlinear Anal. Theory, 21, 77, 10.1016/0362-546X(93)90179-V
Chung, 1994, Finite element Galerkin solutions for the Rosenau equation, Appl. Anal., 54, 39, 10.1080/00036819408840267
Chunk, 2001, Numerical methods for the Rosenau equation, Appl. Anal., 77, 351, 10.1080/00036810108840914
Choo, 2008, A discontinuous Galerkin method for the Rosenau equation, Appl. Numer. Math., 58, 783, 10.1016/j.apnum.2007.02.008
Danumjaya, 2019
Omrani, 2008, A new conservative finite difference scheme for the Rosenau equation, Appl. Math. Comput., 201, 35
Manickam, 1998, A second order splitting combined with orthogonal cubic spline collocation method for the Rosenau equation, Numer. Methods Partial Differential Equations, 14, 695, 10.1002/(SICI)1098-2426(199811)14:6<695::AID-NUM1>3.0.CO;2-L
Erbay, 2021, A semi-discrete numerical method for convolution-type unidirectional wave equations, J. Comput. Appl. Math., 387, 10.1016/j.cam.2019.112496
Zuo, 2009, Solitons and periodic solutions for the Rosenau-KdV and Rosenau-Kawahara equations, Appl. Math. Comput., 215, 835
Erbay, 2020, Numerical computation of solitary wave solutions of the Rosenau equation, Wave Motion, 98, 10.1016/j.wavemoti.2020.102618
Zeng, 2003, Existence and stability of solitary wave solutions of equations of Benjamin Bona Mahony type, J. Differential Equations, 188, 1, 10.1016/S0022-0396(02)00061-X
Patera, 1977, Subalgebras of real three-and four-dimensional Lie algebras, J. Math. Phys., 18, 1449, 10.1063/1.523441
Byrd, 2013
Petviashvili, 1976, Equation of an extraordinary soliton, Fiz. Plazmy. Phys., 2, 469
Pelinovski, 2004, Convergence of Petviashvili’s iteration method for numerical approximation of stationary solutions of nonlinear wave equations, SIAM J. Numer. Anal., 42, 1110, 10.1137/S0036142902414232
Yang, 2010, Nonlinear waves in integrable and nonintegrable systems, Soc. Ind. Appl. Math.
Kawahara, 1972, Oscillatory solitary waves in dispersive media, J. Phys. Soc. Japan, 33, 260, 10.1143/JPSJ.33.260
Khusnutdinova, 2018, Soliton solutions to the fifth-order Korteweg-de Vries equation and their applications to surface and internal water waves, Phys. Fluids, 30, 10.1063/1.5009965
Bona, 2000, Models for internal waves in deep water, Discrete Contin. Dyn. Syst., 6, 1, 10.3934/dcds.2000.6.1
