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...

We describe wave propagation and soliton localization in photonic lattices, which are induced in a nonlinear medium by an optical interference pattern, taking into account the inherent lattice deformations at the soliton location. We obtain exact analytical solutions and identify the key factors defining soliton mobility, including the effects of gap merging and lattice imbalance, underlying th...

In this paper, we use the Riemann–Hilbert (RH) approach to examine integrable three-coupled Lakshmanan–Porsezian–Daniel (LPD) model, which describes dynamics of alpha helical protein with interspine coupling at fourth-order dispersion term. Through spectral analysis Lax pair, construct higher-order matrix RH problem for LPD when jump particular is a $$4\times 4$$ unit matrix, exact N-soliton so...

The Kadomtsev-Petviashvili (KP) equation describes weakly dispersive and small amplitude waves propagating in a quasi-two dimensional situation. Recently a large variety of exact soliton solutions of the KP equation has been found and classified. Those soliton solutions are localized along certain lines in a two-dimensional plane and decay exponentially everywhere else, and they are called line...

The Darboux–Dressing Transformations developed in [1] are here applied to construct soliton solutions for a class of boomeronic–type equations. The vacuum (i.e. vanishing) solution and the generic plane wave solution are both dressed to yield one soliton solutions. The formulae are specialised to the particularly interesting case of the resonant interaction of three waves, a well-known model wh...

This paper obtains the soliton solutions to the Boussinesq equation with the effect of surface tension being taken into account. The power law nonlinearity is considered. Three integration tools are adopted in order to extract the soliton solutions. They are the traveling wave hypothesis, ansatz method and the semi-inverse variational principle. Finally, the Lie symmetry approach is adopted to ...

We consider a simple SU(2) quark soliton model based on chiral invariant quark-meson couplings. We nd axially symmetric, classically stable soliton solutions with B=2,3 and 4 (where B is the baryon number). The energy distributions corresponding to these solutions are toroidal in nature. The symmetries of the B=2 solution indicate that the ground state of this solution has the quantum numbers o...

The analytical solutions for a (2+1)-dimensional breaking solution equation is proposed in this paper by using mapping and projective method darboux transformation, and Some exact propagating solutions are constructed for this Breaking equation, and the M × N multi-soliton could be obtained by using Weierstrassp function and setting the perfect parameters. The potential application of breaking ...

We find new solutions, including soliton-like ones, for a special case of nonAbelian loop Toda equations associated with complex general linear groups. We use the method of rational dressing based on an appropriate block-matrix representation suggested by the Z-gradation under consideration. We present solutions in a form of a direct matrix generalization of the Hirota’s soliton solution alread...

We consider a nonrelativistic Chern-Simons theory of planar matter fields interacting with the Chern-Simons gauge field in a SU(N)global×U(1)local invariant fashion. We find that this model admits static zero-energy selfdual soliton solutions. We also present a set of exact soliton solutions. The exact time-dependent solutions are also obtained, when this model is considered in the background o...