Related papers: Soliton solutions for Q3
This paper extends the results of the previous paper designated I hereafter in which the one- and two-soiton solutions of the Degasperis-Procesi(DP) equation were obtained and their peakon limit was considered. Here, we present the general…
We formulate the $N$ soliton solution of the Wadati-Konno-Ichikawa equation that is determined by purely algebraic equations. Derivation is based on the matrix Riemann-Hilbert problem. We give examples of one soliton solution that include…
Soliton solutions of non-linear NLS and KdV equations are related to compatibility condition between matrices M and H describing the movement of an auxilary function Psi in the x,t plane with a zero curvature condition. Non-linear equation…
A direct method is developed for constructing the bright $N$-soliton solution of a multi-component modified nonlinear Schr\"odinger equation. Specifically, the two different expressions of the solution are obtained both of which are…
A generalized derivative nonlinear Schr\"odinger equation, \ii q_t + q_{xx} + 2\ii \gamma |q|^2 q_x + 2\ii (\gamma-1)q^2 q^*_x + (\gamma-1)(\gamma-2)|q|^4 q = 0 , is studied by means of Hirota's bilinear formalism. Soliton solutions are…
Regarding $N$-soliton solutions, the trigonometric type, the hyperbolic type, and the exponential type solutions are well studied. While for the elliptic type solution, we know only the one-soliton solution so far. Using the commutative…
In the paper we derive rational solutions for the lattice potential modified Korteweg-de Vries equation, and Q2, Q1($\delta$), H3($\delta$), H2 and H1 in the Adler-Bobenko-Suris list. B\"acklund transformations between these lattice…
We consider Novikov's Camassa-Holm type equation with cubic nonlinearity. In particular, we present a compact parametric representation of the smooth bright multisolution solutions on a constant background and investigate their structure.…
Soliton Solutions of Korteweg-de Vries (KdV) were constructed for given degenerate curves $y^2 = (x-c)P(x)^2$ in terms of hyperelliptic sigma functions and explicit Abelian integrals. Connection between sigma functions and tau function were…
We give an elementary introduction to Hirota's direct method of constructing multisoliton solutions to integrable nonlinear evolution equations. We discuss in detail how this works for equations in the Korteweg-de Vries class. We also show…
We study standard and nonlocal nonlinear Schr\"{o}dinger (NLS) equations obtained from the coupled NLS system of equations (Ablowitz-Kaup-Newell-Segur (AKNS) equations) by using standard and nonlocal reductions respectively. By using the…
In this paper, we construct $K$-solitons of the focusing energy-critical nonlinear wave equation in five-dimensional space, i.e. solutions $u$ of the equation such that \begin{equation*}…
Extending the gauge-invariance principle for $\tau$ functions of the standard bilinear formalism to the supersymmetric case, we define ${\cal N}=1$ supersymmetric Hirota bilinear operators. Using them we bilinearize supersymmetric nonlinear…
We establish a correspondence between Darboux's special isothermic surfaces of type (A,0,C,D) and the solutions of the second order PDE : u\Delta(u)-|\nabla(u)|^{2}+\Phi^{4}=s, s \in R. We then use the classical Darboux transformation for…
We use the microscopic instanton calculus to determine the one-instanton contribution to the quantum modulus u_3=<Tr(\phi^3)> in N=2 SU(N_c) supersymmetric QCD with N_f<2N_c fundamental flavors. This is compared with the corresponding…
We study the energy-critical wave equation in three dimensions, focusing on its ground state soliton, denoted by $W$. Using the Poincar\'e symmetry inherent in the equation, boosting $W$ along any timelike geodesic yields another solution.…
We establish the Soliton Resolution Conjecture for the radial critical non-linear heat equation in dimension $D\geq 3.$ Thus, every finite energy solution resolves, continuously in time, into a finite superposition of asymptotically…
Continuously symmetric solutions of the Adler-Bobenko-Suris class of discrete integrable equations are presented. Initially defined by their invariance under the action of both of the extended three point generalized symmetries admitted by…
Quaternion-valued solutions to the non-commutative KdV equation are produced using determinants. The solutions produced in this way are (breather) soliton solutions, rational solutions, spatially periodic solutions and hybrids of these…
The dynamics of soliton and quasisoliton solutions of cubic third order nonlinear Schr\"{o}dinger equation is studied. The regular solitons exist due to a balance between the nonlinear terms and (linear) third order dispersion; they are not…