62 citations · 167 across the 32 of their papers we have counts for
27 papers · 1 filter
Soliton-Generating -Functions Revisited
Yair Zarmi
Within the framework of the Inverse-Scattering formalism and the Hirota algorithm, soliton solutions of evolution equations are images of τ-functions. Typically, the latter are exp…
Traveling waves and localized structures: An alternative view of nonlinear evolution equations
Yair Zarmi
Given a nonlinear evolution equation in (1+n) dimensions, which has spatially extended traveling wave solutions, it can be extended into a system of two coupled equations, one of w…
Kadomtsev-Petviashvili II equation: Structure of asymptotic soliton webs
S. Horowits, Y. Zarmi
A wealth of observations, recently supported by rigorous analysis, indicate that, asymptotically in time, most multi-soliton solutions of the Kadomtsev-Petviashvili II equation sel…
Nonlinear quantum-mechanical system associated with Sine-Gordon equation in (1+2) dimensions
Yair Zarmi
Despite the fact that it is not integrable, the 1 + 2-dimensional Sine-Gordon equation has N-soliton solutions, whose velocities are lower than the speed of light (c = 1), for all…
Sine-Gordon equation in higher dimensions: A fresh look at integrability
Yair Zarmi
The Sine-Gordon equation is integrable in (1+1)-dimensional Minkowski and in 2-dimensional Euclidean spaces. In each case, it has a Lax pair, and a Hirota algorithm generates its N…
Vertex dynamics in multi-soliton solutions of Kadomtsev-Petviashvili II equation
Yair Zarmi
A functional of the solution of the Kadomtsev-Petviashvili II equation maps multi-soliton solutions onto systems of vertices - structures that are localized around soliton junction…
Relativistic particle-like structures associated with multi-soliton solutions of (1+2)-dimensional Sine-Gordon equation
Yair Zarmi
The Sine-Gordon equation in (1+2) dimensions has N-soliton solutions that propagate at velocities that are lower than the speed of light (c = 1), for any N greater tha or equal to…
On multi soliton solutions of the Sine-Gordon equation in more than one space dimension
Yair Zarmi
The (1+1)-dimensional Sine-Gordon equation passes integrability tests commonly applied to nonlinear evolution equations. Its soliton solutions are obtained by a Hirota algorithm. I…
Static solitons, Lorentz invariance, and a new perspective on the integrability of the Sine Gordon equation in (1+2) dimensions
Yair Zarmi
Contrary to the common understanding, the Sine-Gordon equation in (1+2) dimensions does have N-soliton solutions for any N. The Hirota algorithm allows for the construction of stat…
Spatially extended particles hidden in line-soliton dynamics in more than one space dimension
Yair Zarmi
A dynamics of spatially extended particles, hidden in the dynamics of line solitons in more than one space dimension, is revealed through conservation laws obeyed by the single-sol…
Spatially extended relativistic particles associated with multi-soliton solutions of the Sine-Gordon equation in more than one space dimension
Yair Zarmi
Contrary to the decades-old understanding, SGn, the Sine-Gordon equation in (1+n) dimensions, has N-soliton solutions for any N >= 1, not only for n = 1, but also for n = 2 and 3.…
A nonlinear quantum dynamical system of spin 1/2 particles based on the classical Sine-Gordon Equation
Yair Zarmi
The Hirota transformation for the soliton solutions of the classical Sine-Gordon equation is suggestive of an extremely simple way for the construction of a nonlinear quantum-dynam…
Quantized representation for Kadomtsev-Petviashvili equation on the soliton sector
Yair Zarmi
Exploiting the known structure of soliton solutions, obtained through the Hirota transformation, a quantized representation of the Kadomtsev-Petviashvili (KP) equation on the solit…
Special polynomials and soliton dynamics
Yair Zarmi
Special polynomials play a role in several aspects of soliton dynamics. These are differential polynomials in u, the solution of a nonlinear evolution equation, which vanish identi…
Quantized representation of some nonlinear integrable evolution equations on the soliton sector
Yair Zarmi
The Hirota algorithm for solving several integrable nonlinear evolution equations is suggestive of a simple quantized representation of these equations and their soliton solutions…
Special features of the KdV-Sawada-Kotera equation
Yair Zarmi
The KdV-Sawada-Kotera equation has single-, two- and three-soliton solutions. However, it is not known yet whether it has N-soliton solutions for any N. Viewing it as a perturbed K…
Two-component description of dynamical systems that can be approximated by solitons: The case of the ion acoustic wave equations of Plasma Physics
Yair Zarmi
A new approach to the perturbative analysis of dynamical systems, which can be described approximately by soliton solutions of integrable nonlinear wave equations, is employed in t…
Coupled system description of perturbed KdV equation
Yair Zarmi
In the multiple-soliton case, the freedom in the expansion of the solution of the perturbed KdV equation is exploited so as to transform the equation into a system of two equations…
Freedom in Expansion and Asymptotic Integrability of Perturbed Evolution Equations
Yair Zarmi
It is shown that the emergence of obstacles to asymptotic integrability in the analysis of perturbed evolution equations may, often, be a consequence of the manner, in which the fr…
The Perturbed NLS Equation and Asymptotic Integrability
Yair Zarmi
The perturbed NLS equation is asymptotically integrable if the zero-order approximation to the solution is a single soliton. It is not integrable for any other zero-order solution.…
Freedom in the Expansion and Obstacles to Integrability in Multiple-Soliton Solutions of the Perturbed KdV Equation
Alex veksler, Yair Zarmi
The construction of a solution of the perturbed KdV equation encounters obstacles to asymptotic integrability beyond the first order, when the zero-order approximation is a multipl…
Spontaneously generated waves and obstacles to integrability in perturbed evolution equations
Alex Vekser, Yair Zarmi
The perturbed Burgers and KdV equations are considered. Often, the perturbation excites waves that are different from the solution one is seeking. In the case of the Burgers equati…
Wave interactions and the analysis of the perturbed Burgers equation
Alex Veksler, Yair Zarmi
In multiple-front solutions of the Burgers equation, all the fronts, except for two, are generated through the inelastic interaction of exponential wave solutions of the Lax pair a…
Perturbative analysis of wave interactions in nonlinear systems
Alex Veksler, Yair Zarmi
This work proposes a new way for handling obstacles to asymptotic integrability in perturbed nonlinear PDEs within the method of Normal Forms - NF - for the case of multi-wave solu…