This paper systematically investigates the Lie group analysis method of time-fractional regularized long-wave (RLW) equation with Riemann–Liouville fractional derivative. The vector fields and similarity reductions are obtained. It is shown that governing can be transformed into a ordinary differential new independent variable, where derivatives in Erdèlyi–Kober sense. Furthermore, explicit ana...

Third-order dispersive evolution equations are widely adopted to model one-dimensional long waves and have extensive applications in fluid mechanics, plasma physics nonlinear optics. The typical representatives the KdV equation, Camassa–Holm equation Degasperis–Procesi equation. They share many common features such as complete integrability, Lax pairs bi-Hamiltonian structure. In this paper we ...

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...

An efficient and accurate exponential wave integrator Fourier pseudospectral (EWI-FP) method is proposed and analyzed for solving the symmetric regularized-long-wave (SRLW) equation, which is used for modeling the weakly nonlinear ion acoustic and space-charge waves. The numerical method here is based on a Gautschi-type exponential wave integrator for temporal approximation and the Fourier pseu...

This paper is concerned with the finite element method for the stochastic wave equation and the stochastic elastic equation driven by space-time white noise. For simplicity, we rewrite the two types of stochastic hyperbolic equations into a unified form. We convert the stochastic hyperbolic equation into a regularized equation by discretizing the white noise and then consider the full-discrete ...

Time optimal control of the wave equation is analyzed on the basis of a regularized formulation which is considered as a bilevel optimization problem. For the lower level problems, which are constrained optimal control problems for the wave equation, a detailed sensitivity analysis is carried out. Further a semi-smooth Newton method is analyzed and proved to converge locally superlinearly. Nume...

Abstract In this paper, a general framework of the reduced differential transform method is presented for solving the regularized long wave (RLW) equation. In this method, the solution is calculated in the form of convergent power series with easily computable components. The efficiency of the considered method is illustrated by some examples. The results show that the proposed iteration techni...