The paper concerns capillary-gravity surface waves propagating on a two-dimensional incompressible and inviscid fluid with or without an obstacle placed at flat horizontal bottom. Formally second-order correct model equations, analogous to the first-order KdV equation, are derived under classical assumptions of long wavelength small amplitude waves. equations fifth-order type where bottom intro...

In this investigation, the nonplanar (spherical and cylindrical) modified fifth-order Korteweg–de Vries (nmKdV5) equation, otherwise known as Kawahara equation (nmKE), is solved using ansatz approach. Two general formulas for semi-analytical symmetric approximations are derived recommended methodology. Using obtained approximations, (mK) solitary waves (SWs) cnoidal (CWs) obtained. The fluid eq...

Studied here is the Kawahara equation, a fifth-order Korteweg-de Vries type with time-delayed internal feedback. Under suitable assumptions on time delay coefficients, we prove that solutions of this system are exponentially stable. First, considering damping and delayed system, some restriction spatial length domain, energy goes to $ 0 as t \rightarrow \infty $. After that, by introducing more...

In this article, we use the improved general mapping deformation method based on the generalized Jacobi elliptic functions expansion method with computerized symbolic computation to construct some new exact solutions for some nonlinear partial differential equations via the cubic nonlinear Klein Gordon equation and the modified Kawahara equation. As a result, new generalized Jacobi elliptic fun...

In this article, we analysed the approximate solutions of time-fractional Kawahara equation and modified equation, which describe propagation signals in transmission lines formation nonlinear water waves long wavelength region. An efficient technique, namely natural transform decomposition method, is used present study. Fractional derivatives are considered Caputo, Caputo–Fabrizio, Atangana–Bal...

We analyze and implement fully discrete schemes for periodic initial value problems for a general class of dispersively modified Kuramoto–Sivashinsky equations. Time discretizations are constructed using linearly implicit schemes and spectral methods are used for the spatial discretization. The general case analyzed covers several physical applications arising in multi-phase hydrodynamics and t...