is the natural combination of these equations, describing the free motion of an ndimensional surface in a non-Euclidean space; for instance, the motion of a string that is constrained to lie on a sphere would be given (at least to first approximation) as a wave map. As such, wave maps are one of the fundamental equations used to describe geometric motion, although they are not as well understoo...

This work is concerned with the the stability analysis of the constant stationary solution of the following fully nonlinear parabolic equation: ut+ 1 2u 2 x = f(cuuxx)+lnu, x ∈ (0, l) with ux(0, t) = ux(l, t) = 0, where f is a smooth function satisfying f(0) = 0, f ′ > 0 and f(IR) = IR. In the case where f(s) = ln [ exp(s)−1 s ] , this equation represents the evolution of the perturbations of t...

The thermo-elastic plate system of equations is analysed. The sufficient conditions of existence, uniqueness and continuity dependence on initial data of the Cauchy problem solutions for differentialoperational equation of mixed type (a part of the equation of hyperbolic type, and a part of parabolic type) are given in this paper. If the operational coefficients are suitably chosen, the investi...

‎the water wave generation by wave paddle and a freely falling rigid body are examined by using an incompressible smoothed particle hydrodynamics (isph)‎. ‎in the current isph method‎, ‎the pressure was evaluated by solving pressure poisson equation using a semi-implicit algorithm based on the projection scheme and the source term of pressure poisson equation contains both of divergence free ve...

In this paper, the coupled dispersive (2+1)-dimensional long wave equation is studied. The traveling wave hypothesis yields complexiton solutions. Subsequently, the wave equation is studied with power law nonlinearity where the ansatz method is applied to yield solitary wave solutions. The constraint conditions for the existence of solitons naturally fall out of the derivation of the soliton so...

in this paper, we obtained the 1-soliton solutions of the symmetric regularized long wave (srlw) equation and the (3+1)-dimensional shallow water wave equations. solitary wave ansatz method is used to carry out the integration of the equations and obtain topological soliton solutions the physical parameters in the soliton solutions are obtained as functions of the dependent coefficients. note t...

We consider the perturbation of parabolic operators of the form ∂t + P (x,D) by large-amplitude highly oscillatory spatially dependent potentials modeled as Gaussian random fields. The amplitude of the potential is chosen so that the solution to the random equation is affected by the randomness at the leading order. We show that, when the dimension is smaller than the order of the elliptic pseu...

This work provides stability results in the spatial sup norm for hyperbolic-parabolic loops in one spatial dimension. The results are obtained by an application of the small-gain stability analysis. Two particular cases are selected for the study because they contain challenges typical of more general systems (to which the results are easily generalizable but at the expense of less pedagogical ...

In this paper, the equation of motion for an incompressible transversely isotropic fibre-reinforced elastic solid is derived in terms of a scalar function.   The general solution of the equation of motion is obtained, which satisfies the required radiation condition.  The appropriate traction free boundary conditions are also satisfied by the solution to obtain the required secular equation for...