332 citations · 521 across the 11 of their papers we have counts for
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Hamiltonian Integrability of Two-Component Short Pulse Equations
J. C. Brunelli, S. Sakovich
We obtain the bi-Hamiltonian structure for some of the two-component short pulse equations proposed in the literature to generalize the original short pulse equation when polarized…
Smooth soliton solutions of a new integrable equation by Qiao
Sergei Sakovich
We find a transformation which relates a new third-order integrable nonlinear evolution equation, introduced recently by Qiao, with the well-known modified Korteweg - de Vries equa…
On integrability of the vector short pulse equation
Sergei Sakovich
Using the Painleve analysis preceded by appropriate transformations of nonlinear systems under investigation, we discover two new cases in which the Pietrzyk-Kanattsikov-Bandelow v…
Solitary wave solutions of the short pulse equation
Anton Sakovich, Sergei Sakovich
An exact nonsingular solitary wave solution of the Schafer-Wayne short pulse equation is derived from the breather solution of the sine-Gordon equation by means of a transformation…
Enlarged spectral problems and nonintegrability
Sergei Sakovich
The method of obtaining new integrable coupled equations through enlarging spectral problems of known integrable equations, which was recently proposed by W.-X. Ma, can produce non…
The short pulse equation is integrable
Anton Sakovich, Sergei Sakovich
We prove that the Schafer-Wayne short pulse equation (SPE) which describes the propagation of ultra-short optical pulses in nonlinear media is integrable. First, we discover a Lax…