We show that eigenvalues of the family of Baxter Q-operators for supersymmetric integrable spin chains constructed with the gl(K|M)-invariant R-matrix obey the Hirota bilinear difference equation. The nested Bethe ansatz for super spin chains, with any choice of simple root system, is then treated as a discrete dynamical system for zeros of polynomial solutions to the Hirota equation. Our basic...

The new generalized Harry Dym equation of Z. Popowicz is transformed into the Hirota–Satsuma system of coupled KdV equations.

The new generalized Harry Dym equation of Z. Popowicz is transformed into the Hirota–Satsuma system of coupled KdV equations.

In this present study, the exact traveling wave solutions to the time fractional generalized Hirota-Satsuma coupled KdV system are studied by using the direct algebraic method. The exact and complex solutions obtained during the present investigation are new, whereas literature survey has revealed generalizations of solutions. The solutions obtained during the present work demonstrate the fact ...

The new generalized Harry Dym equation, recently introduced by Z. Popowicz in Phys. Lett. A 317, 260–264 (2003), is transformed into the Hirota–Satsuma system of coupled KdV equations.

We introduce a kind of bilinear differential equations by generalizing Hirota bilinear operators, and explore when the linear superposition principle can apply to the resulting generalized bilinear differential equations. Together with an algorithm using weights, two examples of generalized bilinear differential equations are computed to shed light on the presented general scheme for constructi...

This paper focuses on the exact soliton solutions of (2+1)-dimensional generalized Hirota–Satsuma–Ito equations with time-dependent linear phase speed. Based Painlevé integrability test this equation, condition is determined. Then general N-soliton are constructed by Hirota bilinear method. Not only expressions and their degenerations, but also spatial structures presented for different choices...

Narrow optical dip solutions are investigated when, besides self-phase modulation and group velocity dispersion, also third-order dispersion, nonlinear dispersion, and stimulated Raman scattering are taken into account. By using the inverse scattering transform for the higher-order optical nonlinear Schrödinger (HNLS) equation under Hirota parameter conditions, the dark N-soliton solution is co...

Unifying hierarchies of integrable equations are discussed. They are constructed via generalized Hirota identity. It is shown that the Combescure transformations, known for a long time for the Darboux system and having a simple geometrical meaning, are in fact the symmetry transformations of generalized integrable hierarchies. Generalized equation written in terms of invariants of Combescure tr...