Wave propagation in curved tubular domains is considered. A general version of Webster’s equation is derived from the scattering passive wave equation. More precisely, it is shown that planar averages of a sufficiently smooth solution of the wave equation satisfy the corresponding Webster’s equation when the latter includes additional control signals determined by the solution.

Nonlinear dynamics of wave packets in parity-time-symmetric optical lattices near the phase-transition point is analytically studied. A nonlinear Klein-Gordon equation is derived for the envelope of these wave packets. A variety of phenomena known to exist in this envelope equation are shown to also exist in the full equation, including wave blowup, periodic bound states, and solitary wave solu...

We study the Cauchy problem for the damped wave equation. In a previous paper [16] the author has shown the Lp-Lq estimates between the solutions of the damped wave equation and the solutions of the corresponding heat equation. In this paper, we show new Lp-Lq estimates for the damped wave equation with odd initial data.

The unsmooth boundary will greatly affect motion morphology of a shallow water wave, and a fractal space is introduced to establish a generalized KdV-Burgers equation with fractal derivatives. The semi-inverse method is used to establish a fractal variational formulation of the problem, which provides conservation laws in an energy form in the fractal space and possible solution structures of t...

The simplest equation method presents a wide applicability to handling nonlinear wave equations. In this paper, we establish travelling wave solutions for some nonlinear evolution equations. The simplest equation method is used to construct the travelling wave solutions of new Hamiltonian amplitude equation, (3 + 1)-dimensional generalized KP equation, Burgers-KP equation, coupled Higgs field e...

In this present study analytical method based on Riccati Equation as for converting the Nonlinear Lakshmanan-Porsezian-Daniel (LPD) equation into the nonlinear ODE and finding soliton solutions of this sustem discused. Obtaining solutions are new and obtained from wave transformation. The obtained results show that the presented method is effective and appropriate for solving nonlinear differen...

‎Semidiscrete finite element approximation of a hyperbolic type‎ ‎integro-differential equation is studied. The model problem is‎ ‎treated as the wave equation which is perturbed with a memory term.‎ ‎Stability estimates are obtained for a slightly more general problem.‎ ‎These, based on energy method, are used to prove optimal order‎ ‎a priori error estimates.‎

A Shallow Water Wave-like nonlinear differential equation is considered by using the generalized bilinear equation with the generalized bilinear derivatives 3,x D and 3,t D , which possesses the same bilinear form as the standard shallow water wave bilinear equation. By symbolic computation, four presented classes of rational solutions contain all rational solutions to the resulting Shallow Wat...