The open-closed vertex in the maximally supersymmetric type IIB plane-wave light-cone string field theory is considered and an explicit solution for the bosonic part of the vertex is derived, valid for all values of the mass parameter, μ. This vertex is of relevance to IIB plane-wave orientifolds, as well as IIB plane-wave strings in the presence of D-branes and their gauge theory duals. Method...

The inverse water wave problem of bathymetry detection is the problem of deducing the bottom topography of the seabed from measurements of the water wave surface. In this paper, we present a fully nonlinear method to address this problem. The method starts from the Euler water wave equations for inviscid irrotational fluid flow, without any approximation. Given the water wave height and its fir...

In this paper we introduce the (I, J) similar method for incompressible two-dimensional Euler equations, and obtain a series of explicit (I, J) similar solutions to the incompressible two-dimensional Euler equations. These solutions include all of the twin wave solutions, some new singularity solutions, and some global smooth solutions with a finite energy. We also reveal that the twin wave sol...

An analytic solution of long waves scattering by a cylindrical island mounted on a permeable circular shoal was obtained by solving the linear long wave equation LWE . The solution is in terms of the Bessel function expressed by complex variables. The present solution is suitable for arbitrary bottom configurations described by a power function with two independent parameters. For the case of t...

In this paper we study the random approximate travelling wave solutions of the stochastic KPP equations. Two new properties of the stochastic KPP equations are obtained. We prove the ergodicity that for almost all sample paths, behind the wave front x = γt, the lower limit of 1t ∫ t 0 u(s, x)ds as t → ∞ is positive, and ahead of the wave front, the limit is zero. In some cases, behind the wave ...

The problem of edge waves as an example within classical water-wave theory is described by presenting an overview of some of the theories that have been offered for this phenomenon. The appropriate governing equations and boundary conditions are formulated, and then the important discoveries of Stokes and Ursell, concerning the travelling edge wave, are presented. (We do not address the corresp...

A new max-plus fundamental solution semigroup is presented for a class of lossless wave equations. This new semigroup is developed by employing the action principle to encapsulate the propagation of all possible solutions of a given wave equation in the evolution of the value function of an associated optimal control problem. The max-plus fundamental solution semigroup for this optimal control ...

In the paper, a auxiliary equation expansion method and its a lgorithm is proposed by studying a second order nonlinear ordinary differential equation with a six-degree term.The method is applied to the generalized derivative Schrödinger equation .As a result,some new exact traveling wave solution are obtained which singular solutions,triangular periodic wave solution and Jacobian elliptic func...