Integrable discretisations of Volterra system with multiple branches of dispersion

Two integrable discretizations of general differential-difference coupled Volterra equations with multiple branches of dispersion are constructed using the Hirota bilinear formalism. The multi-soliton solutions are built and discussed for both discretizations and the nonlinear forms of completely discretized Volterra system are recovered.

Complete integrability and complex solitons for generalized Volterra system with branched dispersion

In this paper, we show that complete integrability is preserved in a multicomponent differential-difference Volterra system with branched dispersion relation. Using the Hirota bilinear formalism, we construct multisoliton solutions for a system of coupled [Formula: see text] equations. We also show that one can obtain the same solutions through a periodic reduction starting from a two-dimensional completely integrable generalized Volterra system. For some particular cases, graphical representations of solitons are displayed and stability is discussed using an asymptotic analysis.

Multiple point principle in the general Two-Higgs-Doublet model

Based on the Multiple Point Principle, the Higgs boson mass has been predicted to be 135 ± 9 GeV — more than two decades ago. We study the Multiple Point Principle and its prospects with respect to the Two-Higgs-Doublet model (THDM). Applying the bilinear formalism we show that concise conditions can be given with a classification of different kinds of realizations of this principle. We recover cases discussed in the literature but identify also different realizations of the Multiple Point Principle.

Bilinear approach to supersymmetric AKNS system; multiple dressing of fermionic amplitudes

In this paper, we investigate the super-bilinear formalism and interaction of supersoliton solutions for the supersymmetric AKNS system [H. Aratyn and A. Das, Mod. Phys. Lett. A 13, 1185 (1998)]. It is shown that the super-bilinear form involves an auxiliary fermionic tau function and the supersolitons have less freedom than expected (concerning the dependence on fermionic parameters). Also, the interaction between super-solitons is much more complicated than in the case of real supersymmetric equations (KdV, mKdV, Sawada–Kotera, Sine–Gordon, etc.), involving four types of dressing of the fermionic parameters. These solutions are general compared to the ones found in Ref. 1 which contain no fermionic parameter.

The soliton solutions for semidiscrete complex mKdV equation

The semidiscrete complex modified Korteweg–de Vries equation (semidiscrete cmKdV), which is the second member of the semidiscrete nonlinear Schrődinger hierarchy (Ablowitz–Ladik hierarchy), is solved using the Hirota bilinear formalism. Starting from the focusing case of semidiscrete form of cmKdV, proposed by Ablowitz and Ladik, we construct the bilinear form and build the multi-soliton solutions. The complete integrability of semidiscrete cmKdV, focusing case, is proven and results are discussed.

Stability analysis, soliton waves, rogue waves and interaction phenomena for the (3+1)-dimensional generalized Kadomtsev–Petviashvili equation

In this paper, the (3[Formula: see text]+[Formula: see text]1)-dimensional generalized Kadomtsev–Petviashvili (gKP) equation is discussed, which can be used to describe certain characteristics of soliton in a nonlinear media with weak dispersion. By using the virtue of Bell polynomial, we construct the exact bilinear formalism and soliton wave of the equation, respectively. We also analyze its stability analysis. Moreover, based on the resulting bilinear formalism, we obtain its rouge wave solutions with a direct method. Finally, we also discuss the interaction phenomena between solitary wave solutions and rogue wave solutions. It is hoped that our results can be used to enrich the dynamics of the (3[Formula: see text]+[Formula: see text]1)-dimensional nonlinear wave fields.