It is by now well known that the wave functions of rational solutions to the KP hierarchy which can be achieved as limits of the pure n-soliton solutions satisfy an eigenvalue equation for ordinary differential operators in the spectral parameter. This property is known as “bispectrality” and has proved to be both interesting and useful. In this note, it is shown that certain (non-rational) sol...

‎we study the existence of soliton solutions for a class of‎ ‎quasilinear elliptic equation in $mathbb{textbf{r}}^2$ with critical exponential growth‎. ‎this model has been proposed in the self-channeling of a‎ ‎high-power ultra short laser in matter‎.

as an application of hirota bilinear method, perturbation expansion truncated at different levels is used to obtain exact soliton solutions to (2+1)-dimensional nonlinear evolution equation in much simpler way in comparison to other existing methods. we have derived bilinear form of nonlinear evolution equation and using this bilinear form, bilinear backlund transformations and construction of ...

We find non-BPS solutions of the noncommutative CP 1 model in 2+1 dimensions. These solutions correspond to soliton anti-soliton configurations. We show that the one-soliton one-anti-soliton solution is unstable when the distance between the soliton and the anti-soliton is small. We also construct time-dependent solutions and other types of solutions. E-mail: [email protected] E-mail: na...

We discuss new Majumdar-Papapetrou solutions for the 3+1 Einstein-Maxwell equations, with charged dust acting as the external source of the fields. The solutions satisfy non-linear potential equations which are related to well-known wave equations of 1+1 soliton physics. Although the matter distributions are not localised, they present central structures which may be identified with voids. Talk...

In this paper, the two-dimensional generalized nonlinear Schrödinger equations are introduced with Lax pair. The existence of pair defines integrability for partial differential equation, so integrable. Related to development was understanding that certain coherent structures called solitons play a basic role in phenomena as fluid mechanics, optics relativity, and lattice dynamics. Via Hirota b...

Solitons are an important class of solutions to nonlinear differential equations which appear in different areas physics and applied mathematics. In this study we provide a general overview the Hirota method is one most powerful tool finding multi-soliton wave evaluation equations. Bright dark soliton Schrödinger equation discussed detail

\Nonlinear Schrr odinger Equations, Wavelength Divison Multiplexing and Four Wave Mixing" In the limit of large frequency spacing the multisoliton solutions of the nonlinear Schrr odinger equation (NLS), which models the evolution of nonlinear waves in optical bers, are investigated. In Fourier space the individual pulses are found to always be widely separated, and hence can be easily, measure...

The nonlinear Schrödinger equation (NLSE) is a seminal equation of nonlinear physics describing wave packet evolution in weakly-nonlinear dispersive media. The NLSE is especially important in understanding how high amplitude "rogue waves" emerge from noise through the process of modulation instability (MI) whereby a perturbation on an initial plane wave can evolve into strongly-localised "breat...

A forced Korteweg–de Vries (fKdV) equation can be used to model the surface wave of a twodimensional water flow over a bump when the upstream Froude number is near one. The fKdV model typically has four types of solutions: sub-critical cnoidal waves, sub-critical hydraulic fall, transcritical upstream soliton radiation, and supercritical multiple solitary waves. This paper provides a numerical ...