期刊
NONLINEAR DYNAMICS
卷 85, 期 1, 页码 479-498出版社
SPRINGER
DOI: 10.1007/s11071-016-2700-x
关键词
Perturbed Rosenau-Kawahara-RLW equation with power law nonlinearity; Solitary wave solutions; Sine-cosine method; Conservative finite difference method
资金
- Fundamental Research Funds for the Central Universities
- Program for Young Excellent Talents at Tongji University [2013KJ012]
- Natural Science Foundation of China [11402174]
- Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry
In this paper, we study the solitary wave solution and numerical simulation for the generalized Rosenau-Kawahara-RLW equation with generalized Novikov type nonlinear perturbation, which is an extension of our recent work He and Pan (Appl Math Comput 271:323-336, 2015), He (Nonlinear Dyn 82:1177-1190, 2015). We first derive the exact solitary wave solution for the newly proposed perturbed Rosenau-Kawahara-RLW equation with power law nonlinearity and then develop a three-level linearly implicit difference scheme for solving the equation. We prove that the proposed scheme is energy-conserved, unconditionally stable and second-order convergent both in time and space variables. Finally, numerical experiments are carried out to confirm the energy conservation, the convergence rates of the scheme and effectiveness for long-time simulation.
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