The paper presents two results. First it is shown how the discrete potential modified KdV equation and its Lax pairs in matrix form arise from the Hirota–Miwa equation by a 2-periodic reduction. Then Darboux transformations and binary Darboux transformations are derived for the discrete potential modified KdV equation and it is shown how these may be used to construct exact solutions.
We investigate which three dimensional near-horizon metrics gNH admit a compatible 1-form X such that (X, [gNH ]) defines an Einstein-Weyl structure. We find explicit examples and see that some of the solutions give rise to Einstein-Weyl structures of dispersionless KP type and dispersionless Hirota (aka hyperCR) type.
In this paper, we show that the Garnier system in n-variables has affine Weyl group symmetry of type B (1) n+3. We also formulate the τ functions for the Garnier system (or the Schlesinger system of rank 2) on the root lattice Q(Cn+3) and show that they satisfy Toda equations, Hirota-Miwa equations and bilinear differential equations.
Physically relevant soliton solutions of the resonant nonlinear Schrodinger (RNLS) equation with nontrivial boundary conditions, recently proposed for description of uniaxial waves in a cold collisionless plasma, are considered in the Hirota bilinear approach. By the Madelung representation, the model transformed to the reaction-diffusion analog of the NLS equation for which the bilinear repres...
The hamiltonian formalism is developed for the Sine-Gordon model on the space-time light-like lattice, first introduced by Hirota. The evolution operator is explicitely constructed in the quantum variant of the model, the integrability of corresponding classical finite-dimensional system is established.
presentation 1. Bandyopadhyay, S., Wang, Y., Pai, S.K., Hirota, S., Hosobe, S., Tsukada, T., Miura, K., Takano U., Saito, K., Commes, T., Piquemal, D., Watabe, M., and Watabe K. (2005) The metastasis suppressor gene Drg-1 downregulates the expression of ATF3 in prostate and breast carcinoma. American Association for Cancer Research. Anaheim, CA.
Journal:
:Theoretical and Mathematical Physics2022
We consider a simplest two-dimensional reduction of the remarkable three-dimensional Hirota–Ohta system. The Lax pair system was extended to triad by adding extra third linear equation, whose compatibility conditions with imply another systems: Kulish–Sklyanin (KSS) together its first higher commuting flow, which we can call vector complex mKdV. This means that any common particular solution bo...
Linear superposition principles of hyperbolic and trigonometric function solutions are analyzed for Hirota bilinear equations, with an aim to construct a specific sub-class of N-soliton solutions formulated by linear combinations of hyperbolic and trigonometric functions. An algorithm using weights is discussed and a few illustrative application examples are presented. 2013 Elsevier Inc. All ri...
