We consider the integrable multicomponent coherently coupled nonlinear Schrödinger (CCNLS) equations describing simultaneous propagation of multiple fields in Kerr type nonlinear media. The correct bilinear equations of m-CCNLS equations are obtained by using a non-standard type of Hirota's bilinearization method and the more general bright one solitons with single hump and double hump profiles including special flat-top profiles are obtained. The solitons are classified as coherently coupled solitons and incoherently coupled solitons depending upon the presence and absence of coherent nonlinearity arising due to the existence of the copropagating modes/components. Further, the more general two-soliton solutions are obtained by using this non-standard bilinearization approach and various fascinating collision dynamics are pointed out. Particularly, we demonstrate that the collision among coherently coupled soliton and incoherently coupled soliton displays a nontrivial collision behaviour in which the former always undergoes energy switching accompanied by an amplitude dependent phase-shift and change in the relative separation distance, leaving the latter unaltered. But the collision between coherently coupled solitons alone is found to be standard elastic collision. Our study also reveals the important fact that the collision between incoherently coupled solitons arising in the m-CCNLS system with m = 2 is always elastic, whereas for m > 2 the collision becomes intricate and for this case the m-CCNLS system exhibits interesting energy sharing collision of solitons characterized by intensity redistribution, amplitude dependent phase-shift and change in relative separation distance which is similar to that of the multicomponent Manakov soliton collisions. This suggests that the m-CCNLS system can also be a suitable candidate for soliton collision based optical computing in addition to the Manakov system.

We consider the multicomponent Yajima-Oikawa (YO) system and show that the two-component YO system can be derived in a physical setting of a three-coupled nonlinear Schrödinger (3-CNLS) type system by the asymptotic reduction method. The derivation is further generalized to the multicomponent case. This set of equations describes the dynamics of nonlinear resonant interaction between a one-dimensional long wave and multiple short waves. The Painlevé analysis of the general multicomponent YO system shows that the underlying set of evolution equations is integrable for arbitrary nonlinearity coefficients which will result in three different sets of equations corresponding to positive, negative, and mixed nonlinearity coefficients. We obtain the general bright N -soliton solution of the multicomponent YO system in the Gram determinant form by using Hirotas bilinearization method and explicitly analyze the one-and two-soliton solutions of the multicomponent YO system for the above mentioned three choices of nonlinearity coefficients.We also point out that the 3-CNLS system admits special asymptotic solitons of bright, dark, anti-dark, and gray types, when the long-wave-short-wave resonance takes place. The short-wave component solitons undergo two types of energy-sharing collisions. Specifically, in the two-component YO system, we demonstrate that two types of energy-sharing collisions-(i) energy switching with opposite nature for a particular soliton in two components and (ii) similar kind of energy switching for a given soliton in both components-result for two different choices of nonlinearity coefficients. The solitons appearing in the long-wave component always exhibit elastic collision whereas those of short-wave components exhibit standard elastic collisions only for a specific choice of parameters. We have also investigated the collision dynamics of asymptotic solitons in the original 3-CNLS system. For completeness, we explore the three-soliton interaction and demonstrate the pairwise nature of collisions and unravel the fascinating state restoration property.

Abstract. Bright plane soliton solutions of an integrable (2+1) dimensional (n + 1)-wave system are obtained by applying Hirota's bilinearization method. First, the soliton solutions of a 3-wave system consisting of two short wave components and one long wave component are found and then the results are generalized to the corresponding integrable (n + 1)-wave system with n short waves and single long wave. It is shown that the solitons in the short wave components (say S(1) and S (2) ) can be amplified by merely reducing the pulse width of the long wave component (say L). The study on the collision dynamics reveals the interesting behaviour that the solitons which split up in the short wave components undergo shape changing collisions with intensity redistribution and amplitude-dependent phase shifts. Even though similar type of collision is possible in (1+1) dimensional multicomponent integrable systems, to our knowledge for the first time we report this kind of collisions in (2+1) dimensions. However, solitons which appear in the long wave component exhibit only elastic collision though they undergo amplitude-dependent phase shifts.

This work deals with the dynamics of higher-order rogue waves in a new integrable (2+1)-dimensional Boussinesq equation governing the evolution of high and steep gravity water waves. To achieve this objective, we construct rogue wave solutions by employing Bell polynomial and Hirota’s bilinearization method, along with the generalized polynomial function. Through the obtained rogue wave solutions, we explore the impact of various system and solution parameters in their dynamics. Primarily, these parameters determine the characteristics of rogue waves, including the identification of their type, bright or dark type doubly-localized rogue wave structures and spatially localized rational solitons, and manipulation of their amplitude, depth, and width. Reported results will be encouraging to the studies on the rogue waves in higher dimensional systems as well as to experimental investigations on the controlling mechanism of rogue waves in optical systems, atomic condensates, and deep water oceanic waves.

We consider a general multicomponent (2+1)-dimensional long-wave-short-wave resonance interaction (LSRI) system with arbitrary nonlinearity coefficients, which describes the nonlinear resonance interaction of multiple short waves with a long-wave in two spatial dimensions. The general multicomponent LSRI system is shown to be integrable by performing the Painlevé analysis. Then we construct the exact bright multi-soliton solutions by applying the Hirota's bilinearization method and study the propagation and collision dynamics of bright solitons in detail. Particularly, we investigate the head-on and overtaking collisions of bright solitons and explore two types of energy-sharing collisions as well as standard elastic collision. We have also corroborated the obtained analytical one-soliton solution by direct numerical simulation. Also, we discuss the formation and dynamics of resonant solitons. Interestingly, we demonstrate the formation of resonant solitons admitting breather-like (localized periodic pulse train) structure and also large amplitude localized structures akin to rogue waves coexisting with solitons. For completeness, we have also obtained dark oneand two-soliton solutions and studied their dynamics briefly.

The exact bright one- and two-soliton solutions of a particular type of coherently coupled nonlinear Schrödinger equations, with alternate signs of nonlinearities among the two components, are obtained using the non-standard Hirota's bilinearization method. We find that in contrary to the coherently coupled nonlinear Schrödinger equations with same signs of nonlinearities the present system supports only coherently coupled solitons arising due to an interplay between dispersion and the nonlinear effects, namely, self-phase modulation, cross-phase modulation, and four-wave mixing process, thereby depend on the phases of the two co-propagating fields. The other type of soliton, namely, incoherently coupled solitons which are insensitive to the phases of the co-propagating fields and arise in a similar kind of coherently coupled nonlinear Schrödinger equations but with same signs of nonlinearities are not at all possible in the present system. The present system can support regular solution for the choice of soliton parameters for which mixed coupled nonlinear Schrödinger equations admit only singular solution. Our analysis on the collision dynamics of the bright solitons reveals the important fact that in contrary to the other types of coupled nonlinear Schrödinger systems the bright solitons of the present system can undergo only elastic collision in spite of their multicomponent nature. We also show that regular two-soliton bound states can exist even for the choice for which the same system admits singular one-soliton solution. Another important effect identified regarding the bound solitons is that the breathing effects of these bound solitons can be controlled by tuning the additional soliton parameters resulting due to the multicomponent nature of the system which do not have any significant effects on bright one soliton propagation and also in soliton collision dynamics.

We investigate the dynamics of bright matter wave solitons in spin-1 Bose-Einstein condensates with time modulated nonlinearities. We obtain soliton solutions of an integrable autonomous three-coupled Gross-Pitaevskii (3-GP) equations using Hirota's method involving a non-standard bilinearization. The similarity transformations are developed to construct the soliton solutions of non-autonomous 3-GP system. The non-autonomous solitons admit different density profiles. An interesting phenomenon of soliton compression is identified for kink-like nonlinearity coefficient with Hermite-Gaussian-like potential strength. Our study shows that these non-autonomous solitons undergo non-trivial collisions involving condensate switching.

In this paper, we have studied the integrability nature of a system of three coupled Gross-Pitaevskii type nonlinear evolution equations arising in the context of spinor Bose-Einstein condensates by applying the Painlevé singularity structure analysis. We show that only for two sets of parametric choices, corresponding to the known integrable cases, the system passes the Painlevé test.