We take into account here the stochastic-fractional Broer–Kaup equations (SFBKEs) perturbed by multiplicative Wiener process. To get rational, hyperbolic, and elliptic stochastic solutions for SBKEs, we utilize Jacobi function method. The derived are significantly more useful effective in comprehending various important challenging physical phenomena due to of SFBKEs describing propagation shal...

We construct a new multi-component CKP hierarchy based on the eigenfunction symmetry reduction. It contains two types of CKP equation with self-consistent sources which Lax representations are presented. Also it admits reductions to k−constrained CKP hierarchy and to a (1+1)-dimensional soliton hierarchy with self-consistent source, which include two types of Kaup-Kuperschmidt equation with sel...

We consider the modulationally stable version of Kaup–Boussinesq system which models propagation nonlinear waves in various physical situations. It is shown that Whitham modulation equations for this model have a new type solutions describe trigonometric shock waves. In Gurevich–Pitaevskii problem evolution an initial discontinuity, these correspond to nonzero wave excitation on one sides disco...

Gorsky et al. presented an explicit construction of Whitham deformations of the Seiberg-Witten curve for the SU(N+1) N = 2 SUSY Yang-Mills theory. We extend their result to all classical gauge groups and some other cases such as the spectral curve of the A (2) 2N affine Toda Toda system. Our construction, too, uses fractional powers of the superpotential W (x) that characterizes the curve. We a...

To study a nonlinear partial differential equation (PDE), the Painlev́e expansion developed by Weiss, Tabor and Carnevale (WTC) is one of the most powerful methods. In this paper, using any singular manifold, the expansion series in the usual Painlev́e analysis is shown to be resummable in some different ways. A simple nonstandard truncated expansion with a quite universal reduction function is u...

We obtain new gauge-invariant forms of two-dimensional integrable systems of nonlinear equations: the Sawada–Kotera and Kaup–Kuperschmidt system, the generalized system of dispersive long waves, and the Nizhnik–Veselov–Novikov system. We show how these forms imply both new and well-known two-dimensional integrable nonlinear equations: the Sawada–Kotera equation, Kaup–Kuperschmidt equation, disp...

— Kaup-Newell soliton hierarchy is derived from a kind of Lax pairs different from the original ones. Binary nonlinearization procedure corresponding to the Bargmann symmetry constraint is carried out for those Lax pairs. The proposed Lax pairs together with adjoint Lax pairs are constrained as a hierarchy of commutative, finite dimensional integrable Hamiltonian systems in the Liouville sense,...