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119 papers · 1 filter
Residual Symmetry Reductions and Painlevé Solitons
Yan Li, Ya-Rong Xia, Ruo-Xia Yao +1
This letter introduces the novel concept of Painlevé solitons -- waves arising from the interaction between Painlevé waves and solitons in integrable systems. Painlevé solitons may…
Bäcklund-Darboux Transformations for Super KdV Type Equations
Lingling Xue, Shasha Wang, Qing Ping Liu
By introducing a Miura transformation, we derive a generalized super modified Korteweg-de Vries (gsmKdV) equation from the generalized super KdV (gsKdV) equation. It is demonstrate…
Progresses on some open problems related to infinitely many symmetries
S. Y. Lou
The quest to reveal the physical essence of the infinitely many symmetries and conservation laws that are intrinsic to integrable systems has historically posed a significant chall…
Multidimensional Nonhomogeneous Quasi-Linear Systems and Their Hamiltonian Structure
Xin Hu, Matteo Casati
In this paper, we investigate multidimensional first-order quasi-linear systems and find necessary conditions for them to admit Hamiltonian formulation. The insufficiency of the co…
Extensions of dark KdV equations: nonhomogeneous classifications, bosonizations of fermionic systems and supersymmetric dark systems
S. Y. Lou
Dark equations are defined as some kinds of integrable couplings with some fields being homogeneously and linearly coupled to others. In this paper, dark equations are extended in…
Ren-integrable and ren-symmetric integrable systems
S. Y. Lou
A new type of symmetry, ren-symmetry describing anyon physics and the corresponding topological physics, is proposed. Ren-symmetry is a generalization of super-symmetry which is wi…