Ken Ichi Maruno

Multi-Dark Soliton Solutions of the Two-Dimensional Multi-Component Yajima–Oikawa Systems

We present a general form of multi-dark soliton solutions of two-dimensional multi-component soliton systems. Multi-dark soliton solutions of the two-dimensional (2D) and one-dimensional (1D) multi-component Yajima-Oikawa (YO) systems, which are often called the 2D and 1D multi-component long wave-short wave resonance interaction systems, are studied in detail. Taking the 2D coupled YO system with two short wave and one long wave components as an example, we derive the general

An integrable semi-discretization of the coupled Yajima-Oikawa system

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Integrable semi-discretizations of the reduced Ostrovsky equation

-dark-dark soliton solution in both the Gram type and Wronski type determinant forms for the 2D coupled YO system via the KP hierarchy reduction method. By imposing certain constraint conditions, the general

Integrable discretizations and self-adaptive moving mesh method for a coupled short pulse equation

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A two-component generalization of the reduced Ostrovsky equation and its integrable semi-discrete analogue

-dark-dark soliton solution of the 1D coupled YO system is further obtained. The dynamics of one dark-dark and two dark-dark solitons are analyzed in detail. In contrast with bright-bright soliton collisions, it is shown that dark-dark soliton collisions are elastic and there is no energy exchange among solitons in different components. Moreover, the dark-dark soliton bound states including the stationary and moving ones are discussed. For the stationary case, the bound states exist up to arbitrary order, whereas, for the moving case, only the two-soliton bound state is possible under the condition that the coefficients of nonlinear terms have opposite signs.

Rational solutions to two- and one-dimensional multicomponent Yajima-Oikawa systems

In the present paper, an integrable semi-discrete analogue of the one-dimensional coupled Yajima--Oikawa system, which is comprised of multicomponent short-wave and one component long-wave, is proposed by using Hirotas bilinear method. Based on the reductions of the B{a}cklund transformations of the semi-discrete BKP hierarchy, both the bright and dark soliton (for the short-wave components) solutions in terms of pfaffians are constructed.

Geometric Formulation and Multi-dark Soliton Solution to the Defocusing Complex Short Pulse Equation

Based on our previous work to the reduced Ostrovsky equation (J. Phys. A 45 355203), we construct its integrable semi-discretizations. Since the reduced Ostrovsky equation admits two alternative representations, one is its original form, the other is the differentiation form, or the short wave limit of the Degasperis-Procesi equation, two semi- discrete analogues of the reduced Ostrovsky equation are constructed possessing the same N-loop soliton solution. The relationship between these two versions of semi-discretizations is also clarified.

An integrable semi-discrete Degasperis-Procesi equation

In the present paper, integrable semi-discrete and fully discrete analogues of a coupled short pulse (CSP) equation are constructed. The key of the construction is the bilinear forms and determinant structure of solutions of the CSP equation. We also construct Nsoliton solutions for the semi-discrete and fully discrete analogues of the CSP equations in the form of Casorati determinant. In the continuous limit, we show that the fully discrete CSP equation converges to the semi-discrete CSP equation, then further to the continuous CSP equation. Moreover, the integrable semi-discretization of the CSP equation is used as a selfadaptive moving mesh method for numerical simulations. The numerical results agree with the analytical results very well.

Integrable Discrete Model for One-Dimensional Soil Water Infiltration

In the present paper, we propose a two-component generalization of the reduced Ostrovsky equation, whose differential form can be viewed as the short-wave limit of a two-component Degasperis-Procesi (DP) equation. They are integrable due to the existence of Lax pairs. Moreover, we have shown that two-component reduced Ostrovsky equation can be reduced from an extended BKP hierarchy with negative flow through a pseudo 3-reduction and a hodograph (reciprocal) transform. As a by-product, its bilinear form and

The Degasperis–Procesi equation, its short wave model and the CKP hierarchy

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