We use extended mapping method and auxiliary equation method for finding new periodic wave solutions of nonlinear evolution equations in mathematical physics, and we obtain some new periodic wave solution for the Boussinesq system and the coupled KdV equations. This method is more powerful and will be used in further works to establish more entirely new solutions for other kinds of nonlinear pa...

In this work, we established exact solutions for some nonlinear evolution equations. The tanhcoth method was used to construct solitary and soliton solutions of (2+1)-dimensional nonlinear evolution equations. The tanh-coth method presents a wider applicability for handling nonlinear wave equations.

The basic mathematical apparatus of nonlinear optics consists of an array of nonlinear PDEs for the complex amplitudes of an envelope of interacting wave trains. In the general case, these equations include linear and nonlinear dissipative terms. However, in many important cases, they are small and can be neglected: therefore the equations are conservative, and the medium is transparent. Accord...

We establish certain null form estimates of Klainerman-Machedon for parametrices of variable coefficient wave equations for the convex obstacle problem, and for wave equations with metrics of bounded curvature. These are then used to prove a local existence theorem for nonlinear Dirichlet-wave equations outside of convex obstacles.

Nonlinear travelling waves and standing waves can computed by discretizing the appropriate partial differential equations and then solving the resulting system of nonlinear algebraic equations. Here, we show that the “small denominator” problem of Kolmogorov– Arnold–Moser (KAM) theory is equally awkward for numerical algorithms. Furthermore, Newton’s iteration combined with continuation in a pa...

The application of the Kudryashov method for finding exact solutions of the high order nonlinear evolution equations is considered. Some classes of solitary wave solutions for the families of nonlinear evolution equations of fifth, sixth and seventh order are obtained. The efficiency of the Kudryashov method for finding exact solutions of the high order nonlinear evolution equations is demonstr...

The OpenSees finite element software framework is extended for simulating fluid–structure interaction (FSI) by the particle finite element method (PFEM). At high levels of the framework, new classes handle meshing and interface detection of the fluid and structure domains and implement the fractional step method in order to solve the governing equations of linear momentum and mass conservation....

in this present work, the kudryashov method and the functional variable method are used to construct exact solutions of the complex kdv equation. the kudryashov method and the functional variable method are powerful methods for obtaining exact solutions of nonlinear evolution equations.

We study the initial-value problem for a general class of nonlinear nonlocal wave equations arising in one-dimensional nonlocal elasticity. The model involves a convolution integral operator with a general kernel function whose Fourier transform is nonnegative. We show that some well-known examples of nonlinear wave equations, such as Boussinesq-type equations, follow from the present model for...

Abstract: Two class of fractional type solutions of Riccati equation are constructed from its three known solutions. These fractional type solutions are used to propose an approach for constructing infinite number of exact traveling wave solutions of nonlinear evolution equations by means of the extended tanh–function method. The infinite number of exact traveling wave solutions of the long–sho...