We discuss the pivotal role played by the nonlinear dispersion in shaping novel, compact and noncompact patterns. It is Ž n. shown that if the normal velocity of a planar curve is Usy k , n)1, where k is the curvature, then the solitary s disturbances may propagate like compactons. We extend the KP and the Boussinesq equations to include nonlinear dispersion to the effect that the new equations...

This paper studies the bifurcations of exact solutions for time–space fractional complex Ginzburg–Landau equation with parabolic law nonlinearity. Interestingly, different parameters, there are kinds first integrals corresponding traveling wave systems. Using method dynamical systems, which is from previous works, we obtain phase portraits In addition, derive parametric representations solitary...

Bipartite quantum systems from the chiral universality classes admit topologically protected zero modes at point defects. However, in two-dimensional systems these states can be difficult to separate from compacton-like localized states that arise from flat bands, formed if the two sublattices support a different number of sites within a unit cell. Here we identify a natural reduction of chiral...

We consider a family of 2-dimensional ODEs of the form Δξ(z)z ′ = fξ(z) depending on a real parameter ξ which was investigated by Vladimirov [Rep. Math. Phys., 61 (2008), pp. 381–400]. In this system, there exist stationary points pξ which belong to the set of zeros of Δξ. We prove, using rigorous numerics, the existence of a homoclinic orbit to pξ for some parameter value ξ = ξh. Due to the si...

The traveling wave solutions of a generalized HD type equation are investigated in this study. system is singular the first class with given parameter conditions. From standpoint dynamical systems, bifurcations space examined. It demonstrated that solitary solutions, periodic peakons, pseudo-peakons, and compacton exist. All conceivable exact explicit parametric representations various presented.

For the baby Skyrme model with a specific potential, compacton solutions, i.e., configurations with a compact support and parabolic approach to the vacuum, are derived. Specifically, in the non-topological sector, we find spinning Q-balls and Q-shells, as well as peakons. Moreover, we obtain compact baby skyrmions with non-trivial topological charge. All these solutions may form stable multi-so...

In this paper, the variational iteration method (VIM) is reintroduced with Laplace transforms and the Padé technique treatment to obtain closed form solutions of nonlinear equations. Some examples, including the coupled Burger’s equation, compacton k(n, n) equation, Zakharov–Kuznetsov Zk(n, n) equation, and KdV and mKdV equations are given to show the effectiveness of the coupled VIM–Laplace–Pa...

Abstract In this paper, the functional variable method is used to obtain new optical soliton solutions for perturbed stochastic nonlinear Schrödinger equation with generalized anti-cubic nonlinearity and multiplicative white noise. Using some transformations, rational, Jacobi elliptic, Weierstrass, hyperbolic are obtained. Several were proposed, including dark, bright, compacton solutions. Grap...

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