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The successful implementation of a finite element model for computing shallow-water flow requires the identification and spatial discretization of a surface water region. Since no robust criterion or node spacing routine exists, which incorporates physical characteristics and subsequent responses into the mesh generation process, modelers are left to rely on crude gridding criteria as well as t...

We study exchange of stability in the dynamics of solitary wave solutions under changes in the nonlinear balance in a 1+1 evolutionary partial differential equation related both to shallow water waves and to turbulence. We find that solutions of the equation mt + umx + b uxm = ν mxx with m = u − α2uxx for fluid velocity u(x, t) change their behavior at the special values b = 0,±1,±2,±3. PACS nu...

In this study, the generalized (3+1)-dimensional Shallow Water-Like (SWL) equation, which is one of evolution equations, taken into consideration. With help equation discussed, modified Kudryashov method, traveling wave solutions are successfully obtained. these solutions, graphs solitary waves to be obtained by giving special values arbitrary parameters presented. At same time, effect change v...

On the basis of critical analysis of literature it is shown that the existing theory of surface gravity waves is incorrect and contradictory. Based on the new results published by the author dispersive equation for linear waves generated on the surface of tangential discontinuity between air and water was obtained. It is demonstrated that this equation is applicable only to capillary waves and ...

A mathematical model is derived to describe the generation and propagation of water waves by a submarine landslide. The model consists of a depth-integrated continuity equation and momentum equations, in which the ground movement is the forcing function. These equations include full nonlinear, but weak frequencydispersion, e¬ects. The model is capable of describing wave propagation from relativ...

We study the singularly perturbed (sixth-order) Boussinesq equation recently introduced by Daripa and Hua [Appl. Math. Comput. 101 (1999), 159-207]. This equation describes the bi-directional propagation of small amplitude and long capillary-gravity waves on the surface of shallow water for Bond number less than but very close to 1/3. On the basis of far-field analyses and heuristic arguments, ...

This paper obtains solitary waves, shock waves and singular solitons alon with conservation laws of the Rosenau Kortewegde Vries regularized long wave (R-KdV-RLW) equation with power law nonlinearity that models the dynamics of shallow water waves. The ansatz approach and the semi-inverse variational principle are used to obtain these solutions. The constraint conditions for the existence of so...

Finite element solutions of the shallow water wave equations have found increasing use by researchers and practitioners in the modeling of oceans and coastal areas. Wave equation models successfully eliminate spurious oscillation modes without resorting to artificial or numerical damping. Typically, wave equation models integrate the continuity equation with a three-time-level scheme centered a...

Nonlinear partial differential equations are more suitable to model many physical phenomena in science and engineering. In this paper, we consider three nonlinear partial differential equations such as Novikov equation, an equation for surface water waves and the Geng-Xue coupled equation which serves as a model for the unidirectional propagation of the shallow water waves over a flat bottom. T...