55 research outputs found
Explicit travelling wave solutions of two nonlinear evolution equations
In this paper, we applied the sine-cosine method and the rational functions in exp(ksi) method for the modified Kawachara
equation and the Damped Sixth-order Boussinesq Equation, respectively. New solitons solutions and periodic solutions are explicitly
obtained with the aid of symbolic computation
Finite volume methods for unidirectional dispersive wave model
We extend the framework of the finite volume method to dispersive unidirectional water wave propagation in one space dimension. In particular, we consider a KdVâBBM-type equation. Explicit and implicitâexplicit RungeâKutta-type methods are used for time discretizations. The fully discrete schemes are validated by direct comparisons to analytic solutions. Invariantsâ conservation properties are also studied. Main applications include important nonlinear phenomena such as dispersive shock wave formation, solitary waves, and their various interaction
Singularites in the Bousseneq equation and in the generalized KdV equation
In this paper, two kinds of the exact singular solutions are obtained by the
improved homogeneous balance (HB) method and a nonlinear transformation. The
two exact solutions show that special singular wave patterns exists in the
classical model of some nonlinear wave problems
Finite volume methods for unidirectional dispersive wave models
We extend the framework of the finite volume method to dispersive
unidirectional water wave propagation in one space dimension. In particular we
consider a KdV-BBM type equation. Explicit and IMEX Runge-Kutta type methods
are used for time discretizations. The fully discrete schemes are validated by
direct comparisons to analytic solutions. Invariants conservation properties
are also studied. Main applications include important nonlinear phenomena such
as dispersive shock wave formation, solitary waves and their various
interactions.Comment: 25 pages, 12 figures, 51 references. Other authors papers can be
downloaded at http://www.lama.univ-savoie.fr/~dutykh
New Exact Solutions of a Generalized Shallow Water Wave Equation
In this work an extended elliptic function method is proposed and applied to
the generalized shallow water wave equation. We systematically investigate to
classify new exact travelling wave solutions expressible in terms of
quasi-periodic elliptic integral function and doubly-periodic Jacobian elliptic
functions. The derived new solutions include rational, periodic, singular and
solitary wave solutions. An interesting comparison with the canonical procedure
is provided. In some cases the obtained elliptic solution has singularity at
certain region in the whole space. For such solutions we have computed the
effective region where the obtained solution is free from such a singularity.Comment: A discussion about singularity and some references are added. To
appear in Physica Script
New exact traveling wave solutions for the KleinâGordonâZakharov equations
AbstractBased on the extended hyperbolic functions method, we obtain the multiple exact explicit solutions of the KleinâGordonâZakharov equations. The solutions obtained in this paper include (a) the solitary wave solutions of bell-type for u and n, (b) the solitary wave solutions of kink-type for u and bell-type for n, (c) the solitary wave solutions of a compound of the bell-type and the kink-type for u and n, (d) the singular traveling wave solutions, (e) periodic traveling wave solutions of triangle function types, and solitary wave solutions of rational function types. We not only rederive all known solutions of the KleinâGordonâZakharov equations in a systematic way but also obtain several entirely new and more general solutions. The variety of structures of the exact solutions of the KleinâGordonâZakharov equations is illustrated
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