Symmetry reductions and traveling wave solutions for the Krichever-Novikov equation

2012 ◽  
Vol 35 (8) ◽  
pp. 869-876 ◽  
Author(s):  
M.S. Bruzón ◽  
M.L. Gandarias
Keyword(s):  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Symmetry Reductions ◽  
Wave Solutions ◽  
Novikov Equation

scholarly journals Single peaked traveling wave solutions to a generalized μ-Novikov Equation

2020 ◽  
Vol 10 (1) ◽  
pp. 66-75
Author(s):  
Byungsoo Moon
Keyword(s):  
Linear Combination ◽  
Traveling Wave ◽  
Wave Solution ◽  
Traveling Wave Solutions ◽  
Traveling Wave Solution ◽  
Wave Solutions ◽  
Quadratic Nonlinearities ◽  
Novikov Equation

Abstract In this paper, we study the existence of peaked traveling wave solution of the generalized μ-Novikov equation with nonlocal cubic and quadratic nonlinearities. The equation is a μ-version of a linear combination of the Novikov equation and Camassa-Hom equation. It is found that the equation admits single peaked traveling wave solutions.

Exact Cuspon and Compactons of the Novikov Equation

2014 ◽  
Vol 24 (03) ◽  
pp. 1450037 ◽  
Author(s):  
Jibin Li
Keyword(s):  
Dynamical Systems ◽  
Qualitative Analysis ◽  
Traveling Wave ◽  
Wave Solution ◽  
Traveling Wave Solutions ◽  
Phase Portraits ◽  
Breaking Wave ◽  
Wave Solutions ◽  
Novikov Equation

In this paper, we apply the method of dynamical systems to the traveling wave solutions of the Novikov equation. Through qualitative analysis, we obtain bifurcations of phase portraits of the traveling system and exact cuspon wave solution, as well as a family of breaking wave solutions (compactons). We find that the corresponding traveling system of Novikov equation has no one-peakon solution.

scholarly journals Lie Symmetry Analysis, Traveling Wave Solutions, and Conservation Laws to the (3 + 1)-Dimensional Generalized B-Type Kadomtsev-Petviashvili Equation

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Huizhang Yang ◽  
Wei Liu ◽  
Yunmei Zhao
Keyword(s):  
Conservation Laws ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Lie Symmetry Analysis ◽  
Symmetry Reductions ◽  
Wave Solutions ◽  
Petviashvili Equation ◽  
Bkp Equation

In this paper, the (3 + 1)-dimensional generalized B-type Kadomtsev-Petviashvili(BKP) equation is studied applying Lie symmetry analysis. We apply the Lie symmetry method to the (3 + 1)-dimensional generalized BKP equation and derive its symmetry reductions. Based on these symmetry reductions, some exact traveling wave solutions are obtained by using the tanh method and Kudryashov method. Finally, the conservation laws to the (3 + 1)-dimensional generalized BKP equation are presented by invoking the multiplier method.

Symmetry Reductions and Exact Solutions to the Kudryashov–Sinelshchikov Equation

2016 ◽  
Vol 71 (11) ◽  
pp. 1059-1065 ◽  
Author(s):  
Huizhang Yang
Keyword(s):  
Exact Solutions ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Explicit Solutions ◽  
Bifurcation Method ◽  
Characteristic Equations ◽  
Symmetry Reductions ◽  
Wave Solutions ◽  
Nonclassical Symmetries

AbstractIn this article, based on the compatibility method, some nonclassical symmetries of Kudryashov–Sinelshchikov equation are derived. By solving the corresponding characteristic equations associated with symmetry equations, some new exact explicit solutions of Kudryashov–Sinelshchikov equation are obtained. For the exact explicit traveling wave solutions, the exact parametric representations are investigated by the integral bifurcation method.

Exact Traveling Wave Solutions of the Krichever–Novikov Equation: A Dynamical System Approach

2017 ◽  
Vol 27 (04) ◽  
pp. 1750058 ◽  
Author(s):  
KitIan Kou ◽  
Jibin Li
Keyword(s):  
Traveling Wave ◽  
Invariant Manifolds ◽  
Solitary Wave Solution ◽  
Dynamical Behavior ◽  
Traveling Wave Solutions ◽  
Periodic Wave ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Painlevé Property ◽  
Novikov Equation

In this paper, we show that to find the traveling wave solutions for the Krichever–Novikov equation, we only need to consider a spatial form F-VI of the fourth-order differential equations in the polynomial class having the Painlevé property given by [Cosgrove, 2000]. By using the method of dynamical systems to analyze the dynamical behavior of the traveling wave solutions in some two-dimensional invariant manifolds, various exact solutions such as solitary wave solution, periodic wave solutions, quasi-periodic wave solutions and uncountably infinitely many unbounded wave solutions are obtained.

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