We consider the zero-dispersion limit for Benjamin–Ono equation on torus. prove that when initial data is bell shaped, exists in weak sense and uniform every compact time interval. Moreover, equal to signed sum of branches multivalued solution inviscid Burgers obtained by method characteristics. This result similar one Miller Xu real line decaying positive data. also establish some precise asym...

Steady, supersonic, dissipative, three-dimensional, axisymmetric flow is considered. A system of Burgers-type equations is shown to govern the flow field. In inviscid regions the Whitham theory gives the limiting form. Dissipative effects ultimately engulf the inviscid zone and at sufficiently large distances from the body the flow is governed by linear dissipative theory. The flow field is div...

To avoid un-realistic solutions like expansion shocks from appearing as a part of a solution it is necessary to satisfy the entropy condition for the Roe scheme. A variety of entropy fix formulae for the Roe scheme have been addressed in the literature. Three of the most famous are due to Harten-Hyman and Hoffmann-Chiang. These formulations have been assessed in this paper by applying them to t...

In this paper, the modified simplest equation method is successfully implemented to find travelling wave solutions of the generalized forms $B(n,1)$ and $B(-n,1)$ of Burgers equation. This method is direct, effective and easy to calculate, and it is a powerful mathematical tool for obtaining exact travelling wave solutions of the generalized forms $B(n,1)$ and $B(-n,1)$ of Burgers equation and ...

An overview of a Hamiltonian framework for the description nonlinear modulation surface water waves is presented. The main result derivation version Dysthe’s equation two-dimensional gravity on deep water. reduced problem obtained via Birkhoff normal form transformation which not only helps eliminate all non-resonant cubic terms but also yields non-perturbative procedure reconstruction. free re...