Related papers: Framework for the Forced Soliton Equation: Regular…

We construct one soliton solutions for the nonlinear Schroedinger equation with variable quadratic Hamiltonians in a unified form by taking advantage of a complete (super) integrability of generalized harmonic oscillators. The soliton wave…

Soliton dynamics in a large variety of longitudinally modulated lattices are studied in terms of phase space analysis for an effective particle approach and direct numerical simulations. Complex soliton dynamics are shown to depend strongly…

We study the dynamics of solitons under the action of one-dimensional quasiperiodic lattice potentials, fractional diffraction, and nonlinearity. The formation and stability of the solitons is investigated in the framework of the fractional…

A general and systematic regularization is developed for the exact solitonic form factors of exponential operators in the (1+1)-dimensional sine-Gordon model by analytical continuation of their integral representations. The procedure is…

We consider a family of regularized defocusing nonlinear Schrodinger (NLS) equations proposed in the context of the cubic NLS equation with a bounded dispersion relation. The time evolution is well-posed if the black soliton is perturbed by…

We study the exact statistical mechanics of Lam\'e solitons using a transfer matrix method. This requires a knowledge of the first forbidden band of the corresponding Schr\"odinger equation with the periodic Lam\'e potential. Since the…

Simulating the real-time dynamics of quantum field theories (QFTs) is one of the most promising applications of quantum simulators. Regularizing a bosonic QFT for quantum simulation purposes typically involves a truncation in Hilbert space…

We show that quantum effects can stabilize a soliton in a model with no soliton at the classical level. The model has a scalar field chirally coupled to a fermion in 1+1 dimensions. We use a formalism that allows us to calculate the exact…

We study various properties of the soliton solutions of the modified regularized long-wave equation. This model possesses exact one- and two-soliton solutions but no other solutions are known. We show that numerical three-soliton…

We will give a short introduction to discrete or lattice soliton equations, with the particular example of the Korteweg-de Vries as illustration. We will discuss briefly how B\"acklund transformations lead to equations that can be…

We give a pedagogical introduction to Linearized Soliton Perturbation Theory (LSPT), a new and efficient tool for calculations involving quantum solitons. It is a Hamiltonian approach with a focus on explicitly constructing the soliton…

We present an analytical and numerical study of the Klein-Gordon kink-soliton dynamics in inhomogeneous media. In particular, we study an external field that is almost constant for the whole system but that changes its sign at the center of…

We analytically study plasma solitary waves, or solitons, in a two-dimensional (2D) electron system (ES) placed in close proximity to and between two ideal metallic gates. As a rule, solitons are described using a perturbative approach…

We consider an hierarchy of integrable 1+2-dimensional equations related to Lie algebra of the vector fields on the line. The solutions in quadratures are constructed depending on $n$ arbitrary functions of one argument. The most…

We explore the classical production of solitons in the easy axis O(3) model in 1+1 dimensions, for a wide range of initial conditions that correspond to the scattering of small breathers. We characterize the fractal nature of the region in…

The main objective of this thesis has been to analyse soliton dynamics in detail, with special attention paid to the role of the internal modes associated with these configurations. Specifically, the thesis has focused on the study of one-…

We study stability of a generalized sine-Gordon model with two coupled scalar fields in two dimensions. Topological soliton solutions are found from the first-order equations that solve the equations of motion. The perturbation equations…

Affine Toda field theory with a pure imaginary coupling constant is a non-hermitian theory. Therefore the solutions of the equation of motion are complex. However, in $1+1$ dimensions it has many soliton solutions with remarkable…

We present a detailed numerical study of the stability under periodic perturbations of line solitons of two-dimensional, generalized Zakharov-Kuznetsov equations with various power nonlinearities. In the $L^{2}$-subcritical case, in…

We present a method to obtain soliton solutions to relativistic system of coupled scalar fields. This is done by examining the energy associated to static field configurations. In this case we derive a set of first-order differential…