6,209 research outputs found
New Exact solution for the (2+1)-dimensional Dispersive Long Wave
Abstract: First Integral method obtains some exact solution of non-integrable equations as well as integrable ones. This article is concerned with First Integral method for solving the solution of dispersive long wave system. It is worth mentioning that this method is based on the theory of commutative algebra in which division theorem is of concern. To recapitulate, this investigation has resulted in two exact soliton solutions of the given system. In addition, some figures of partial solutions are provided for direct-viewing analysis. The method can also be extended to other types of nonlinear evolution equations in mathematical physics.Keywords: First Integral method; Exact solution; Dispersive long wave (2+1)-dimensiona
A nonlinear transformation of the dispersive long wave equations in (2+1) dimensions and its applications
A nonlinear transformation of the dispersive long wave equations in (2+1)
dimensions is derived by using the homogeneous balance method. With the aid of
the transformation given here, exact solutions of the equations are obtained
Exact analytical solution of viscous Korteweg-deVries equation for water waves
The evolution of a solitary wave with very weak nonlinearity which was
originally investigated by Miles [4] is revisited. The solution for a
one-dimensional gravity wave in a water of uniform depth is considered. This
leads to finding the solution to a Korteweg-de Vries (KdV) equation in which
the nonlinear term is small. Also considered is the asymptotic solution of the
linearized KdV equation both analytically and numerically. As in Miles [4], the
asymptotic solution of the KdV equation for both linear and weakly nonlinear
case is found using the method of inversescattering theory. Additionally
investigated is the analytical solution of viscous-KdV equation which reveals
the formation of the Peregrine soliton that decays to the initial sech^2(\xi)
soliton and eventually growing back to a narrower and higher amplitude
bifurcated Peregrine-type soliton.Comment: 15 page
A symmetry classification for a class of (2+1)-nonlinear wave equation
In this paper, a symmetry classification of a -nonlinear wave equation
where is a smooth function on , using
Lie group method, is given. The basic infinitesimal method for calculating
symmetry groups is presented, and used to determine the general symmetry group
of this -nonlinear wave equation
Abundant Exact Traveling Wave Solutions of the (2+1)-Dimensional Couple Broer-Kaup Equations
To describe the propagation of small amplitude waves in nonlinear dispersive media, it is frequently necessary to take account of dissipative mechanisms to perfectly reflect real situations in many branches of physics like plasma physics, fluid dynamics and nonlinear optics. In this paper, the exp(-Fi(Eta))-expansion method is employed to solve the (2+1)-Dimensional couple Broer-Kaup equations as a model for wave propagation in nonlinear media with dispersive and dissipative effects. As a result, a number of exact traveling wave solutions including solitary wave and periodic wave have been found for the equation. Some representative 3D profiles and 2D profiles for different values of variables of the wave solutions are graphically displayed and discussed
Wave group dynamics in weakly nonlinear long-wave models
Wave group dynamics is studied in the framework of the extended
Korteweg-de Vries equation. The nonlinear Schrodinger equation is derived for
weakly nonlinear wave packets, and the condition for modulational instability
is obtained. It is shown that wave packets are unstable only for a positive sign
of the coefficient of the cubic nonlinear term in the extended Korteweg-de Vries
equation, and for a high carrier frequency. At the boundary of this parameter
space, a modified nonlinear Schrodinger equation is derived, and its steady-state
solutions, including an algebraic soliton, are found. The exact breather solution
of the extended Korteweg-de Vries equation is analyzed. It is shown that in
the limit of weak nonlinearity it transforms to a wave group with an envelope
described by soliton solutions of the nonlinear Schrodinger equation and its
modification as described above. Numerical simulations demonstrate the main
features of wave group evolution and show some differences in the behavior of
the solutions of the extended Korteweg-de Vries equation, compared with those
of the nonlinear Schrodinger equation
Solitary wave fission and fusion in the (2+1)-dimensional generalized Broer–Kaup system
Via a special Painlevé–Bäcklund transformation and the linear superposition theorem, we derive the general variable separation solution of the (2 + 1)-dimensional generalized Broer–Kaup system. Based on the general variable separation solution and choosing some suitable variable separated functions, new types of V-shaped and A-shaped solitary wave fusion and Y-shaped solitary wave fission phenomena are reported
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