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Continuous groups of transformations acting on the expanded space of variables, which includes the equation parameters in addition to independent and dependent variables, are considered. It is shown that the use of the expanded transformations enables one to enrich the concept of similarity reductions of PDEs. The expanded similarity reductions of… (More)

Similarity solutions for laminar two-fluid jets and wakes are derived in the boundary-layer approximation. Planar and axisymmetric fan jets as well as classical and momentumless planar wakes are considered. The interface between the immiscible fluids is stabilized by the action of gravity, with the heavier fluid, taken to be a liquid, placed beneath the… (More)

A new approach to the problem of asymptotic integrability of physical systems is developed and applied to the KdV equation with higher-order corrections. A central object of the approach is an integrable reference equation, which is constructed by defining a proper Lie– Bäcklund group of transformations and applying it to the leading order equation. It is… (More)

- Georgy I. Burde
- Chaos
- 2012

Some new effects in the soliton dynamics governed by higher order Korteweg-de Vries (KdV) equations are discussed based on the exact explicit solutions of the equations on the positive half-line. The solutions describe the process of generation of a soliton that occurs without boundary forcing and on the steady state background: the boundary conditions… (More)

- Georgy I. Burde
- Physical review. E, Statistical, nonlinear, and…
- 2011

Some effects in the soliton dynamics governed by higher-order Korteweg-de Vries (KdV) type equations are discussed. This is done based on the exact explicit solutions of the equations derived in the paper. It is shown that some higher order KdV equations possessing multisoliton solutions also admit steady state solutions in terms of algebraic functions… (More)

The modern view, that there exists a preferred frame of reference related to the cosmic microwave background (CMB), is in apparent contradiction with the principles of special relativity. The purpose of the present study is to develop a counterpart of the special relativity theory that is consistent with the existence of a preferred frame but, like the… (More)

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