Here we show that weakly nonlinear flexural-gravity wave packets, such as those propagating on the surface of ice-covered waters, admit three-dimensional fully localized solutions that travel with a constant speed without dispersion or dissipation. These solutions, that are formed at the intersection of line-soliton mean-flow tracks, have exponentially decaying tails in all directions and are c...

Induced surfaces and their integrable dynamics. II. Generalized Weierstrass representations in 4D spaces and deformations via DS hierarchy. Abstract Extensions of the generalized Weierstrass representation to generic surfaces in 4D Euclidean and pseudo-Euclidean spaces are given. Geometric characteristics of surfaces are calculated. It is shown that integrable deformations of such induced surfa...

This paper concerns the sharp threshold of blowup and global existence of the solution as well as the strong instability of standing wave eu(x) to the system iφt +Δφ+ a|φ|p−1φ+ bE1(|φ|)φ = 0 (DS) in R , where a > 0, b > 0, 1 ≤ p < N+2 (N−2)+ , N ∈ {2, 3} and u is a ground state. First, by constructing a type of cross-constrained variational problem and establishing so-called cross-invariant man...

in this work g&apos;/g-expansion method has been employed to solve (2+1)-dimensional dispersive long wave equation. it is shown that g&apos;/g-expansion method, with the help of symbolic computation, provides a very effective and powerful mathematical tool, for solving this equation.

We give an overview of the basic physical concepts and analytical methods for investigating the symmetrybreaking instabilities of solitary waves. We discuss self-focusing of spatial optical solitons in di!ractive nonlinear media due to either transverse (one more unbounded spatial dimension) or modulational (induced by temporal wave dispersion) instabilities, in the framework of the cubic nonli...

A direct rational exponential scheme is offered to construct exact multi-soliton solutions of nonlinear partial differential equation. We have considered the Calogero–Bogoyavlenskii–Schiff equation and KdV equation as two concrete examples to show efficiency of the method. As a result, one wave, two wave and three wave soliton solutions are obtained. Corresponding potential energy of the solito...