Solitons, Shock Waves and Conservation Laws of Rosenau-KdV-RLW Equation with Power Law Nonlinearity

Razborova, Polina; Ahmed, Bouthina S.; Biswas, Anjan

doi:10.12785/amis/080205

Cited by 72 publications

(50 citation statements)

References 17 publications

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“…(36) for u n+1 . We assume that U n+1,1 , U n+1,2 are two solutions of (36). Let W n+1 = U n+1,1 − U n+1,2 , then it is easy to verify that U n+1 satisfies the following equation:…”

Section: Existence and Uniquenessmentioning

confidence: 99%

“…For numerical investigations, [34] proposed a second-order conservative finite difference method for the Rosenau-KdV equation. By coupling the above Rosenau-RLW equation and Rosenau-KdV equation, one can obtain the following Rosenau-KdV-RLW equation [35][36][37][38][39],…”

Section: Introductionmentioning

confidence: 99%

“…For theoretical studies, [36][37][38][39] studied the solitary wave, shock waves, conservation laws as well as the asymptotic behavior for the Rosenau-KdV-RLW equation with power law nonlinearity.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

New solitary solutions and a conservative numerical method for the Rosenau–Kawahara equation with power law nonlinearity

2015

Nonlinear Dyn

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Recently, Biswas et al. (Phys Wave Phenom 19:24-29, 2011) derived exact bright and dark solitary solutions for the Rosenau-Kawahara equation with power law nonlinearity, and Hu et al. (Adv Math Phys 11, Article ID 217393, 2014) proposed two conservative finite difference schemes for the usual RosenauKawahara equation. In this paper, we obtain another set of exact solitary solutions for the Rosenau-Kawahara equation with power law nonlinearity. More importantly, a conservative finite difference method is presented. The fundamental energy conservation law is preserved by the current numerical scheme. And the existence and uniqueness of the numerical solution are proved. The convergence and stability of the numerical solution are also shown. The method is second-order convergent both in time and in space. Finally, numerical results confirm well with the theoretical results and show that the current method can be well used to study the solitary wave at long time.

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“…(36) for u n+1 . We assume that U n+1,1 , U n+1,2 are two solutions of (36). Let W n+1 = U n+1,1 − U n+1,2 , then it is easy to verify that U n+1 satisfies the following equation:…”

Section: Existence and Uniquenessmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

New solitary solutions and a conservative numerical method for the Rosenau–Kawahara equation with power law nonlinearity

2015

Nonlinear Dyn

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“…Study of these models has reported quite interesting results, which are available in literature [3,12,14,15,19].…”

Section: Introductionmentioning

confidence: 99%

Numerical Study of Rosenau-KDV Equation Using Finite Element Method Based on Collocation Approach

Dhawan

Karakoç

et al. 2017

Mathematical Modelling and Analysis

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Abstract. In the present paper, a numerical method is proposed for the numerical solution of Rosenau-KdV equation with appropriate initial and boundary conditions by using collocation method with septic B-spline functions on the uniform mesh points. The method is shown to be unconditionally stable using von-Neumann technique. To check accuracy of the error norms L2 and L∞ are computed. Interaction of two and three solitary waves are used to discuss the effect of the behavior of the solitary waves during the interaction. Furthermore, evolution of solitons is illustrated by undular bore initial condition. These results show that the technique introduced here is suitable to investigate behaviors of shallow water waves.

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“…Recently, the Rosenau-KdV-RLW equation was proposed in [25] as a conjunction of Rosenau-KdV and Rosenau-RLW equations both of which are well studied and explained with regard to shallow water waves.…”

Section: Introductionmentioning

confidence: 99%

Chebyshev Rational Approximations for the Rosenau-KdV-RLW Equation on the Whole Line

2018

ijaa

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Abstract. In this paper, we consider the use of a modified Chebyshev rational approximations for the Rosenau-KdV-RLW equation on the whole line with initial-boundary values. It is shown that the proposed scheme leads to optimal error estimates. Furthermore, the stability and convergence of the proposed schemes are proved. The fully discrete Chebyshev pseudo-spectral scheme is constructed. Numerical results confirm well with the theoretical results. The idea and techniques presented in this paper will be useful to solve many other problems.

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Solitons, Shock Waves and Conservation Laws of Rosenau-KdV-RLW Equation with Power Law Nonlinearity

Cited by 72 publications

References 17 publications

New solitary solutions and a conservative numerical method for the Rosenau–Kawahara equation with power law nonlinearity

New solitary solutions and a conservative numerical method for the Rosenau–Kawahara equation with power law nonlinearity

Numerical Study of Rosenau-KDV Equation Using Finite Element Method Based on Collocation Approach

Chebyshev Rational Approximations for the Rosenau-KdV-RLW Equation on the Whole Line

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