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Article
Coupled modified KdV equations, skew orthogonal polynomials, convergence acceleration algorithms and Laurent property
In this paper, we show that the coupled modified KdV equations possess rich mathematical structures and some remarkable properties. The connections between the system and skew orthogonal polynomials, convergen...
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Article
Integrable discretization of soliton equations via bilinear method and Bäcklund transformation
We present a systematic procedure to derive discrete analogues of integrable PDEs via Hirota’s bilinear method. This approach is mainly based on the compatibility between an integrable system and its Bäcklund ...
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Article
One variant of a (2 + 1)-dimensional Volterra system and its (1 + 1)-dimensional reduction
A new system is generated from a multi-linear form of a (2+1)-dimensional Volterra system. Though the system is only partially integrable and needs additional conditions to possess two-soliton solutions, its (...
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Article
Convergence acceleration algorithms related to a generalized E-transformation and its particular cases
In this paper, a generalized E-transformation arising from the study of a generalization of sequence transformations and triangular recursion schemes is proposed. Three new algorithms, namely, the generalized ...
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Article
Open AccessNew type of Nonisospectral KP Equation with Self-Consistent Sources and its Bilinear Bäcklund Transformation
A new type of the nonisospectral KP equation with self-consistent sources is constructed by using the source generation procedure. A new feature of the obtained nonisospectral system is that we allow y-dependence...
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Article
Open AccessConstruction of q-discrete two-dimensional Toda lattice equation with self-consistent sources
The q-discrete two-dimensional Toda lattice equation with self-consistent sources is presented through the source generalization procedure. In addition, the Gramm-type determinant solutions of the system are o...
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Article
A Gradient-based Continuous Method for Large-scale Optimization Problems
In this paper, we study a gradient-based continuous method for large-scale optimization problems. By converting the optimization problem into an ODE, we are able to show that the solution trajectory of this O...
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Article
Open AccessPfaffianization of the q-difference version of the two-dimensional Toda lattice equation
We apply the pfaffianization procedure to the q-difference version of the two-dimensional Toda lattice equation to produce the pfaffian analogue of the q-difference two-dimensional Toda lattice equation. A sol...
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Article
Open AccessSome Recent Results on Integrable Bilinear Equations
This paper shows that several integrable lattices can be transformed into coupled bilinear differential-difference equations by introducing auxiliary variables. By testing the Bäcklund transformations for this...
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Article
Limits of parallelism in explicit ODE methods
Numerical methods for ordinary initial value problems that do not depend on special properties of the system are usually found in the class of linear multistage multivalue methods, first formulated by J.C. But...
