We show that a left-invariant metric g on a nilpotent Lie group N is a soliton metric if and only if a matrix U and vector v associated the manifold (N, g) satisfy the matrix equation Uv = [1], where [1] is a vector with every entry a one. We associate a generalized Cartan matrix to the matrix U and use the theory of Kac-Moody algebras to analyze the solution spaces for such linear systems. We ...

We shed light on the fundamental form of the Peregrine soliton as well as on its frequency chirping property by virtue of a pertinent cubic-quintic nonlinear Schrödinger equation. An exact generic Peregrine soliton solution is obtained via a simple gauge transformation, which unifies the recently-most-studied fundamental rogue-wave species. We discover that this type of Peregrine soliton, viabl...

Abstract In this study, we present two different methods a sech-tanh method and extended tanh-method to obtained the soliton solutions of the two-dimensional Korteweg-de Vries-Burgers (KdVB) equation with the initial conditions. These solutions include bright and dark solitary wave solutions, triangular solutions and complex line soliton wave solution. These solutions are stable and have applic...

We construct static, asymptotically flat solutions of SU(2) Einstein-Yang-Mills theory in 4 + 1 dimensions, subject to bi-azimuthal symmetry. Both particle-like and black hole solutions are considered for two different sets of boundary conditions in the Yang–Mills sector, corresponding to multisolitons and soliton-antisoliton pairs. For gravitating multi-soliton solutions, we find that their ma...

An analytical model for the soliton-potential interaction is presented, by constructing a collective coordinate for the system. Most of the characters of the interaction are derived analytically while they are calculated by other models numerically. We will find that the behaviour of the soliton is like a point particle ’living’ under the influence of a complicated potential which is a function...

Propagation of incoherent nonlinear picosecond pulses in a single-mode optical fiber is considered within the framework of the nonlinear Schrijdinger equation. Statistical characteristics of a non-soliton wave packet induced by a random input pulse are obtained with the help of the inverse scattering technique. The probability of a soliton creation from the random pulse is found. Mean soliton a...

We extend the dispersion-velocity particle method that we recently introduced to advection models in which the velocity does not depend linearly on the solution or its derivatives. An example is the Korteweg de Vries (KdV) equation for which we derive a particle method and demonstrate numerically how it captures soliton–soliton interactions.