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Exactly Solvable Models in Statistical Mechanics
Recent studies on exactly solvable models in statistical mechanics are reviewed. A brief summary of the quantum inverse scattering method is given to emphasize the soliton theoretic aspect of the…
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Asymmetric simple exclusion process with open boundaries and Askey–Wilson polynomials
We study the one-dimensional asymmetric simple exclusion process (ASEP) with open boundary conditions. Particles are injected and ejected at both boundaries. It is clarified that the steady state of…
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Simple Derivation of Bäcklund Transformation from Riccati Form of Inverse Method
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Exact analysis of soliton dynamics in spinor Bose-Einstein condensates.
TLDR
It is proved that the system possesses a completely integrable point leading to the existence of multiple bright solitons and a collision law for two-soliton solutions is analyzed and found that the dynamics can be explained in terms of the spin precession.
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Multipartite entanglement and hyperdeterminants
TLDR
This work classifies multipartite entanglement in a unified manner, focusing on a duality between the set of separable states and that of entangled states, and suggests that hyperdeterminants, derived from the duality, are natural generalizations of entangling measures, the concurrence, 3- tangle for 2, 3 qubits respectively.
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Correlation Functions of Random Matrix Ensembles Related to Classical Orthogonal Polynomials. III
TLDR
This work systematically evaluates the correlation functions of the random matrix ensembles in all the three cases of complex hermitian, real symmetric and self-dual quaternion random matrices.
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The Modified Korteweg-de Vries Equation
It is shown that the Modified Korteweg-de Vries equation can be solved exactly by the “inverse scattering method.” As the special case, the N -soliton solution is obtained explicitly. It is found…
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Introduction to solitons
As an introduction to the special issue on nonlinear waves, solitons and their significance in physics are reviewed. The soliton is the first universal concept in nonlinear science. Universality and…
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Stochastic Korteweg-de Vries Equation
The Korteweg-de Vries equation with external noise is studied. It is shown that a soliton under Gaussian noise satisfies a diffusion equation in transformed coordinates. The deformation of the…
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Transformation Theories for Nonlinear Discrete Systems
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