A substantial part of the energy of wake waves from high-speed ships sailing in shallow water is concentrated in nonlinear components which at times have a solitonic nature. Recent results of investigations into solitonic wave interactions within the framework of the Kadomtsev-Petviashvili equation and their implications for rogue wave theory are reviewed. A surface elevation four times as high...

This research paper targets the fractional Hirota’s analytical solutions–Satsuma (HS) equations. The conformable derivative is employed to convert system into a with an integer–order. extended simplest equation (ESE) and modified Kudryashov (MKud) methods are used construct novel solutions of considered model. solutions’ accuracy investigated by handling computational Adomian decomposition meth...

The superposition formulas of multi-solutions to the (3+1)-dimensional generalized shallow water wave-like Equation (GSWWLE) are proposed. There arbitrary test functions in mixed solutions and interaction solutions, we sum any N terms. By freely selecting positive integer N, have obtained abundant for GSWWLE. First, introduced new between two multi-kink solitons, were through symbolic computati...

Keywords: Ocean wave modeling Uncertainty quantification Generalized polynomial chaos Sparse grid collocation Sensitivity analysis Karhunen–Loeve decomposition a b s t r a c t The primary objective of this study is to introduce a stochastic framework based on generalized polynomial chaos (gPC) for uncertainty quantification in numerical ocean wave simulations. The techniques we present can be e...

A one-dimensional hybrid numerical model is presented of a shallow-water flume with an incorporated piston paddle. The hybrid model is based on the improved Boussinesq equations by Madsen and Sørensen (1992) and the nonlinear shallow water equations. It is suitable for breaking and non-breaking waves and requires only two adjustable parameters: a friction coefficient and a wave breaking paramet...

in this work g'/g-expansion method has been employed to solve (2+1)-dimensional dispersive long wave equation. it is shown that g'/g-expansion method, with the help of symbolic computation, provides a very effective and powerful mathematical tool, for solving this equation.

The purpose of this letter is to investigate the geometry of new classes of solitonlike solutions for integrable nonlinear equations. One example is the class of peakons introduced by Camassa and Holm [1993] for a shallow water equation. We put this equation in the framework of complex integrable Hamiltonian systems on Riemann surfaces and using special limiting procedures, draw some consequenc...