Journal ArticleDOI
Kawahara equation and modified Kawahara equation with time dependent coefficients: symmetry analysis and generalized G′G-expansion method
Lakhveer Kaur,R. K. Gupta +1 more
TLDR
In this paper, the similarity reductions and exact solutions are derived by determining the complete sets of point symmetries of these equations, and some exact analytic solutions are considered by the power series method.Abstract:
In this paper, variable coefficients Kawahara equation (VCKE) and variable coefficients modified Kawahara equation (VCMKE), which arise in modeling of various physical phenomena, are studied by Lie group analysis. The similarity reductions and exact solutions are derived by determining the complete sets of point symmetries of these equations. Moreover, some exact analytic solutions are considered by the power series method. Further, a generalized -expansion method is applied to VCKE and VCMKE for constructing some new exact solutions. As a result, hyperbolic function solutions, trigonometric function solutions and some rational function solutions with parameters are furnished. Copyright © 2012 John Wiley & Sons, Ltd.read more
Citations
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Dynamical analysis of lump solutions for (3 + 1) dimensional generalized KP–Boussinesq equation and Its dimensionally reduced equations
Lakhveer Kaur,Abdul-Majid Wazwaz +1 more
TL;DR: In this article, a new form of the (3 + 1) dimensional generalized Kadomtsev-Petviashvili (KP)-Boussinesq equation was proposed for exploring lump solutions by making use of its Hirota bilinear form.
Journal ArticleDOI
Lie symmetry reductions and group invariant solutions of (2 + 1)-dimensional modified Veronese web equation
Sachin Kumar,Amit Kumar +1 more
TL;DR: In this article, the authors applied the Lie symmetry method to compute group invariant solutions for the modified Veronese web (mVw) equation and obtained its infinitesimals, commutation table of Lie algebra, symmetry reductions and closed form analytical solutions.
Journal ArticleDOI
Bright – dark optical solitons for Schrödinger-Hirota equation with variable coefficients
Lakhveer Kaur,Abdul-Majid Wazwaz +1 more
TL;DR: In this paper, the Schrodinger-Hirota equation (SHE) is used to regulate the proliferation of solitons in diverse variety of dispersive optical fibers.
Journal ArticleDOI
Lie symmetry analysis and generalized invariant solutions of (2+1)-dimensional dispersive long wave (DLW) equations
TL;DR: In this article, the authors apply the Lie group of point transformation method to construct the generalized invariant solutions for the (2+1)-dimensional dispersive long wave (DLW) equations under some constraints imposed on infinitesimal generators.
Journal ArticleDOI
Painlevé analysis and invariant solutions of generalized fifth-order nonlinear integrable equation
Lakhveer Kaur,Abdul-Majid Wazwaz +1 more
TL;DR: In this article, a generalized fifth-order nonlinear integrable equation has been investigated by locating movable critical points with aid of Painleve analysis and it has been found that this equation passes painleve test for $$\alpha =\beta $$ which implies affirmation toward the complete integrability.
References
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Book
Principles of mathematical analysis
TL;DR: The real and complex number system as discussed by the authors is a real number system where the real number is defined by a real function and the complex number is represented by a complex field of functions.
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
Symmetries and differential equations
TL;DR: In this article, the maximal Lie group or abstract monoid of symmetries of an ordinary non-singular differential equation (or system of equations) allows us to obtain solutions of them.