N = 2 supersymmetric U(N) Yang-Mills theory softly broken to N = 1 by the superpotential of the adjoint scalar fields is discussed from the viewpoint of the Whitham deformation theory for prepotential. With proper identification of the superpotential we derive the matrix model curve from the condition that the mixed second derivatives of the Whitham prepotential have a nontrivial kernel. e-mail...

The paper contains some new results and a review of recent achievements, concerning the multisupport solutions to matrix models. In the leading order of the ’t Hooft expansion for matrix integral, these solutions are described by quasiclassical or generalized Whitham hierarchies and are directly related to the superpotentials of four-dimensional N = 1 SUSY gauge theories. We study the derivativ...

In this work, three models of the nonlinear Schrödinger equation are looked at to see if traveling wave solutions have unique structures. “The generalized Korteweg–de Vries, (2+1)-dimensional Ablowitz–Kaup–Newell–Segur, and Maccari models” among examined systems. The kinetic energy operator is affected by where mass is, how it changes over time, shown. Using Riccati expansion method, new solito...

We present a way to deal with dispersion-dominated “shock-type” transition in the absence of completely integrable structure for the systems that one may characterize as strictly hyperbolic regularized by a small amount of dispersion. The analysis is performed by assuming that, the dispersive shock transition between two different constant states can be modelled by an expansion fan solution of ...

Under the traveling wave transformation, Fornberg-Whitham equation is reduced to an ordinary differential equation whose general solution can be obtained using the factorization technique. Furthermore, we apply the change of the variable and complete discrimination system for polynomial to solve the corresponding integrals and obtain the classification of all single traveling wave solutions to ...