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Direct linearizing transform for three-dimensional discrete integrable systems: the lattice AKP, BKP and CKP
1School of Mathematics, University of Leeds, Leeds LS2 9JT, UK.
Proceedings. Mathematical, Physical, and Engineering Sciences
|August 15, 2017
Summary
A unified framework solves 3D discrete integrable systems like the lattice AKP, BKP, and CKP equations using direct linearizing transforms. This method yields novel soliton solutions for the lattice CKP equation.
Area of Science:
- Mathematical Physics
- Nonlinear Dynamics
- Integrable Systems
Background:
- Discrete integrable systems are crucial in mathematical physics.
- Understanding their solution structures is a key challenge.
- Existing methods may lack a unified approach for 3D systems.
Purpose of the Study:
- To present a unified framework for solving 3D discrete integrable systems.
- To introduce a direct linearizing transform for solution structure analysis.
- To apply this framework to derive new solutions for specific lattice equations.
Main Methods:
- Development of a unified theoretical framework.
- Application of the direct linearizing transform.
- Integral transform techniques for solution mapping.
- Derivation of soliton-type solutions.
Main Results:
- A general class of integral transforms between solutions is established.
- The framework is shown to be applicable to lattice AKP, BKP, and CKP equations.
- Novel soliton-type solutions for the lattice CKP equation are obtained.
Conclusions:
- The direct linearizing transform provides a unified approach to discrete integrable systems.
- This framework facilitates the discovery of new soliton solutions.
- The study advances the understanding of solution structures in 3D integrable systems.
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