Journal ArticleDOI
Traveling‐wave solutions and the coupled Korteweg–de Vries equation
TLDR
In this paper, it was shown that if one of the solutions is of the form v≡v(x−ct), the other also must be of u≡u(x −ct).Abstract:
Some coupled nonlinear equations are considered for studying traveling‐wave solutions. By introducing a stream function Ψ it is shown that if one of the solutions is of the form v≡v(x−ct), the other also must be of the form u≡u(x−ct). In addition, the possibility of including cubic nonlinear terms has been considered and such a system, assuming that the solutions are of the traveling‐wave type, has been solved.read more
Citations
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Journal ArticleDOI
Solitary wave solutions for some systems of coupled nonlinear equations
TL;DR: In this article, the authors give certain types of exact solutions (solitary wave solutions and periodic solutions) of some systems of coupled nonlinear equations by using a special truncated expansion.
Journal ArticleDOI
PT-symmetry breaking in complex nonlinear wave equations and their deformations
TL;DR: In this paper, complex versions of the KortewegdeVries equations and an Ito-type nonlinear system with two coupled nonlinear fields were investigated and rational, trigonometric/hyperbolic and elliptic solutions for these models including those which are physically feasible in an obvious sense, but also those with complex energy spectra.
Journal ArticleDOI
PT-symmetry breaking in complex nonlinear wave equations and their deformations
TL;DR: In this article, complex versions of the Korteweg-deVries equations and an Ito type nonlinear system with two coupled nonlinear fields were investigated and it was shown that the symmetry can be spontaneously broken in two alternative ways either by specific choices of the domain or by manipulating the parameters in the solutions of the model, thus leading to complex energies.
Journal ArticleDOI
Solitary wave solutions of a system of coupled nonlinear equations
TL;DR: In this article, a class of coupled nonlinear wave equations is presented and it is shown that the coupled equation possesses solitary wave solutions, and some comments are made on the previously obtained solutions of a similar class of equations.
Journal ArticleDOI
Remarks on a system of coupled nonlinear wave equations
TL;DR: It has been shown that an increase in nonlinearity in one variable in a particular fashion does not affect the existence of solitary wave solutions in a generalized system of coupled KdV-MKdV equation as mentioned in this paper.
References
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Journal ArticleDOI
Symmetries and conservation laws of a coupled nonlinear wave equation
TL;DR: In this paper, a coupled nonlinear wave equation is presented, and it is shown that the coupled equation possesses infinitely many symmetries and conservation laws, each of which is a hamiltonian system.
Journal ArticleDOI
Cusp Soliton Solutions of the Ito-Type Coupled Nonlinear Wave Equation
TL;DR: The Ito-type coupled nonlinear wave equation is shown to have cusp soliton solutions in this article, where the soliton solution is defined as a singular spiky soliton.