By using gauge transformations, we manage to obtain new solutions of (2 + 1)dimensional Kadomtsev-Petviashvili(KP), Kaup-Kuperschmidt(KK) and SawadaKotera(SK) equations from non-zero seeds. For each of the preceding equations, a Galilean type transformation between these solutions u2 and the previously known solutions u2 generated from zero seed is given. We present several explicit formulas of...

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 o...

C. de Graaf, ∗ C. Sousa, and R. Broer Department of Physical and Inorganic Chemistry, Universitat Rovira i Virgili Plaça Imperial Tàrraco 1, 43005 Tarragona, Spain Departament de Qúımica F́ısica and Parc Cient́ıfic, Universitat de Barcelona C/ Mart́ı i Franquès 1, 08028 Barcelona, Spain Theoretical Chemistry, Materials Science Centre, Rijksuniversiteit Groningen Nijenborgh 4, 9747 AG Groningen, Th...

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 o...

We study the Seiberg-Witten-Whitham equations in the strong coupling regime of the N = 2 super Yang-Mills theory in the vicinity of the maximal singularities. In the case of SU(2) the Seiberg-Witten-Whitham equations fix completely the strong coupling expansion. For higher rank SU(N) they provide a set of non-trivial constraints on the form of this expansion. As an example, we study the off-dia...

We present a fundamental solution to an initial value problem for the KdV-Whitham system in an explicit integral form. Monotonically decreasing initial data with finite number of breaking points are considered. Generating function for the commuting flows of the averaged KdV hieararchy producing the analytical solutions to the KdV-Whitham system is constructed.