Journal ArticleDOI
Soliton Solutions of Deformed Nonlinear Schrödinger Equations Using Ansatz Method
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In this article, the deformation of nonlinear Schrodinger (NLS) type equations, the so-called Camassa-Holm NLS (CH-NLS), and the CamASSa-holm derivative NLS(CH-DNLS) equation are investigated to obtain the solitary waves solutions.Abstract:
In this paper, the deformation of nonlinear Schrodinger (NLS) type equations, the so-called Camassa–Holm NLS (CH-NLS) equation and Camassa–Holm derivative NLS (CH-DNLS) equation are investigated to obtain the solitary waves solutions. These deformed equations are recently constructed using the Lagrangian deformation and loop algebra splittings. The solitary wave ansatz method is used to obtain the exact soliton solutions of these equations. The behaviours of solitons solutions are presented by 3D and 2D graphs.read more
Citations
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Optical solitons in metamaterials with third and fourth order dispersions
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Optical singular and dark solitons to the nonlinear Schrödinger equation in magneto-optic waveguides with anti-cubic nonlinearity
TL;DR: In this paper, the authors investigated the coupled nonlinear Schrodinger equation in magneto-optic waveguides having anti-cubic (AC) law nonlinearity.
Journal ArticleDOI
New optical solitons and modulation instability analysis of generalized coupled nonlinear Schrödinger–KdV system
TL;DR: In this article , the generalized coupled nonlinear Schrödinger-KdV (NLS-KDV) system is investigated to obtain new optical soliton solutions.
Journal ArticleDOI
Exact and explicit traveling wave solutions to the generalized Gardner and BBMB equations with dual high-order nonlinear terms
TL;DR: In this article, the first integral method was used to solve the generalized Gardner and Benjamin-Bona-Mahoney-Burgers (BBMB) equations with dual high-order nonlinear terms.
References
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Journal ArticleDOI
An integrable shallow water equation with peaked solitons
Roberto Camassa,Darryl D. Holm +1 more
TL;DR: A new completely integrable dispersive shallow water equation that is bi-Hamiltonian and thus possesses an infinite number of conservation laws in involution is derived.
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Exp-function method for nonlinear wave equations
Ji-Huan He,Xu-Hong Wu +1 more
TL;DR: In this article, a new method, called Exp-function method, is proposed to seek solitary solutions, periodic solutions and compacton-like solutions of nonlinear differential equations, and the modified KdV equation and Dodd-Bullough-Mikhailov equation are chosen to illustrate the effectiveness and convenience of the suggested method.
Journal ArticleDOI
The (G' G)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics
TL;DR: The (G'/G)-expansion method is firstly proposed in this paper, where G = G(xi) satisfies a second order linear ordinary differential equation (LODE for short), by which the travelling wave solutions involving parameters of the KdV equation, the mKdV equations, the variant Boussinesq equations and the Hirota-Satsuma equations are obtained when the parameters are taken as special values.
Journal ArticleDOI
A sine-cosine method for handlingnonlinear wave equations
TL;DR: A sine-cosine method is used for obtaining traveling wave solutions for nonlinear wave equations with minimal algebra and is applied to selected physical models to illustrate the usage of the main results.