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Article
Open AccessFrom one to infinity: symmetries of integrable systems
Integrable systems constitute an essential part of modern physics. Traditionally, to approve a model is integrable one has to find its infinitely many symmetries or conserved quantities. In this letter, taking...
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Article
Open AccessDeformation conjecture: deforming lower dimensional integrable systems to higher dimensional ones by using conservation laws
Utilizing some conservation laws of (1+1)-dimensional integrable local evolution systems, it is conjectured that higher dimensional integrable equations may be regularly constructed by a deformation algorithm....
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Article
Open AccessDuality of positive and negative integrable hierarchies via relativistically invariant fields
It is shown that the relativistic invariance plays a key role in the study of integrable systems. Using the relativistically invariant sine-Gordon equation, the Tzitzeica equation, the Toda fields and the seco...
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Article
Coherent structure of Alice–Bob modified Korteweg de-Vries equation
To describe two-place events, Alice–Bob systems have been established by means of the shifted parity and delayed time reversal in the preprint ar**v:1603.03975v2
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Article
Open AccessAlice-Bob Physics: Coherent Solutions of Nonlocal KdV Systems
In natural and social science, many events happened at different space-times may be closely correlated. Two events, A (Alice) and B (Bob) are defined correlated if one event is determined by another, say, ...
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Article
Open AccessPrimary Branch Solutions of First Order Autonomous Scalar Partial Differential Equations via Lie Symmetry Approach
A primary branch solution (PBS) is defined as a solution with m independent n − 1 dimensional arbitrary functions for an m order n dimensional partial differential equation (PDE). PBSs of arbitrary first order sc...
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Article
Bosonization, singularity analysis, nonlocal symmetry reductions and exact solutions of supersymmetric KdV equation
Assuming that there exist at least two fermionic parameters, the classical \( \mathcal{N}=1 \) supersymmetric Korteweg-...
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Article
Doubly periodic patterns of modulated hydrodynamic waves: Exact solutions of the Davey-Stewartson system
Exact doubly periodic standing wave patterns of the Davey-Stewartson (DS) equations are derived in terms of rational expressions of elliptic functions. In fluid mechanics, DS equations govern the evolution of ...
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Article
Nonlinear excitations and “peakons” of a (2+1)-dimensional generalized Broer-Kaup system
Shallow water waves and a host of long wave phenomena are commonly investigated by various models of nonlinear evolution equations. Examples include the Korteweg–de Vries, the Camassa–Holm, and the Whitham–Bro...
