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Article
On q-Gaussian Integrable Hamiltonian Reductions in Anisentropic Magneto-gasdynamics
Integrable substructure in 2+1-dimensional anisentropic magneto-gasdynamics is investigated via a general elliptic vortex ansatz. The procedure involves introduction of a q-Gaussian density representation. Thermo...
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Article
On a Bernoulli-integrable magnetohydrodynamic system
A geometric procedure is used to isolate four Bernoulli integrals for a nonlinear, two-dimensional magnetohydrodynamic system. The general solution of the latter may thereby be constructed.
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Article
A novel class of model constitutive laws in nonlinear elasticity: Construction via Loewner theory
Using a solitonic connection, we show that the class of infinitesimal Bäcklund transformations originally introduced by Loewner in 1952 in a gasodynamic context results in physically interesting nonlinear mode...
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Article
Open AccessVortex Trains in Super-Alfvénic Magnetogasdynamics. Application of Reciprocal-Bäcklund Transformations
A multi-parameter class of reciprocal transformations is coupled with the action of a Backlund transformation to construct periodic solutions of breather-type in plane, aligned, super-Alfvénic magnetogasdynami...
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Article
The Kinematics of the Planar Motion of Ideal Fiber-Reinforced Fluids: An Integrable Reduction and Bäcklund Transformation
We establish that the kinematic constraints on the steady planar motion of an ideal fiber-reinforced fluid can be consolidated in a single third-order nonlinear equation. Remarkably, this equation admits a sol...
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Article
Termination of Bergman series. Connection to the Bn Toda System
Truncation of Bergman-type series applied to a canonical hyperbolic equation is shown to lead to the integrable Bn Toda lattice. In particular, the recurrence relations for the truncated Bergman series are implie...
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Chapter
On a Laplace Sequence of Nonlinear Integrable Ernst-Type Equations
Invariance under Laplace-Darboux-type transformations is established for the 2+1-dimensional Loewner-Konopelchenko-Rogers integrable system. This is exploited to derive a chain of novel, integrable Ernst-type ...
