A ( $$3+1$$ )-dimensional generalized shallow water waves equation is investigated with different methods. Based on symbolic computation and Hirota bilinear form, N-soliton solutions are constructed. In the process of degeneration solutions, T-breathers derived by taking complexication method. Then rogue will emerge during breathers parameter limit Through full N-soliton, M-lump based long-wave...

Extending the gauge-invariance principle for τ functions of the standard bilinear formalism to the supersymmetric case, we define N=1 supersymmetric Hirota operators. Using them, we bilinearize SUSY KdV-type equations (KdV, Sawada-Kotera-Ramani, Hirota-Satsuma). The solutions for multiple collisions of super-solitons and extension to SUSY sine-Gordon are also discussed.

Using Painleve singularity structure analysis, we show that coupled higher-order nonlinear Schrodinger (CHNLS) equations admit the Painleve property. Using the results of the Painleve analysis, we succeed in Hirota bilinearizing the CHNLS equations for the integrable cases. Solving the Hirota bilinear equations, one soliton and two soliton solutions are explicitly obtained. Lax pairs are explic...

D-branes constitute an important part of the superstring theory in its nonperturbative description. Especially coincident multi D-brane states enable us to reproduce nonabelian guage theory in the low energy. From the mathematical point of view, on the other hand, a non-perturbative field theory must be formulated within the framework of a completely integrable system, namely a system whose who...

We give a simple proof that the Neumann coefficients of surface states in Witten’s SFT satisfy the Hirota equations for dispersionless KP hierarchy. In a similar way we show that the Neumann coefficients for the three string vertex in the same theory obey the Hirota equations of the dispersionless Toda Lattice hierarchy. We conjecture that the full (dispersive) Toda Lattice hierachy and, even m...

Riemann theta functions are used to construct one-periodic and two-periodic wave solutions to a class of (2 + 1)-dimensional Hirota bilinear equations. The basis for the involved solution analysis is the Hirota bilinear formulation, and the particular dependence of the equations on independent variables guarantees the existence of one-periodic and two-periodic wave solutions involving an arbitr...

In this paper, we obtain some exact solutions of Derivative Reaction-Diffusion (DRD) system and, as by-products, we also show some exact solutions of DNLS via Hirota bilinearization method. At first, we review some results about two by two AKNS-ZS system, then introduce Hirota bilinearization method to find out exact N-soliton solutions of DNLS and exact N-dissipaton solutions of the Derivative...

We prove that one system of coupled KdV equations, recently claimed by Hirota, Hu and Tang [J. Math. Anal. Appl. 288:326–348 (2003)] to pass the Painlevé test for integrability, actually fails the test at the highest resonance of the generic branch. Introduction In Section 6 of their recent work [1], Hirota, Hu and Tang reported that the system of coupled KdV equations ∂ui ∂t + 6a ( N