Journal ArticleDOI
Lie symmetry analysis, optimal system, exact solutions and dynamics of solitons of a ( $$3+1$$ 3 + 1 )-dimensional generalised BKP–Boussinesq equation
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This article is published in Pramana.The article was published on 2022-01-22. It has received 25 citations till now. The article focuses on the topics: Infinitesimal & Lie group.read more
Citations
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Nonlinear elastic circular rod with lateral inertia and finite radius: Dynamical attributive of longitudinal oscillation
TL;DR: In this paper , Wang et al. investigated the dynamical attitude of a nonlinear elastic circular rod's longitudinal oscillation with lateral inertia and finite radius, and the axial symmetry of this model has been thought through by using cylindrical coordinates.
Journal ArticleDOI
Nonlinear self-adjointness, conserved quantities and Lie symmetry of dust size distribution on a shock wave in quantum dusty plasma
Hassan Almusawa,Adil Jhangeer +1 more
TL;DR: In this paper , the authors derived the ( 3 + 1 )-dimensional Zakharov-Kuznetsov burgers equation for the shock wave phenomena in plasma with dust-charged particles having quantum effects.
Journal ArticleDOI
New local and nonlocal soliton solutions of a nonlocal reverse space-time mKdV equation using improved Hirota bilinear method
TL;DR: In this article , the authors derived bright one and two soliton solutions for a nonlocal nonlinear integrable KdV equation using an improved Hirota bilinear method (HBM).
Journal ArticleDOI
A generalized nonlinear fifth-order KdV-type equation with multiple soliton solutions: Painlevé analysis and Hirota Bilinear technique
Sachin Kumar,B. Mohan +1 more
TL;DR: In this paper , a generalized nonlinear KdV-type equation of fifth-order using the recursion operator was formulated. But the authors used the Hirota bilinear technique to construct the solutions for multiple solitons and showed the graphics for these built solutions.
References
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Book
Applications of Lie Groups to Differential Equations
TL;DR: In this paper, the Cauchy-Kovalevskaya Theorem has been used to define a set of invariant solutions for differential functions in a Lie Group.
Book
Solitons, Nonlinear Evolution Equations and Inverse Scattering
M. A. Ablowitz,Peter A. Clarkson +1 more
TL;DR: In this article, the authors bring together several aspects of soliton theory currently only available in research papers, including inverse scattering in multi-dimensions, integrable nonlinear evolution equations in multidimensional space, and the ∂ method.
Book
Darboux transformations and solitons
V. B. Matveev,Mikhail A. Salle +1 more
TL;DR: In this paper, the authors developed a systematic algebraic approach to solve linear and non-linear partial differential equations arising in soliton theory, such as the non-stationary linear Schrodinger equation, Korteweg-de Vries and Kadomtsev-Petviashvili equations, the Davey Stewartson system, Sine-Gordon and nonlinearSchrodinger equations 1+1 and 2+1 Toda lattice equations, and many others.
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.
Related Papers (5)
New symmetry reductions and exact solutions of the Davey–Stewartson system. I. Reductions to ordinary differential equations
Peter A. Clarkson,Simon Hood +1 more