相关论文: Collective coordinates for the hybrid model

We consider the interaction of solitary waves in a model involving the well-known $\phi^4$ Klein-Gordon theory, but now bearing both Laplacian and biharmonic terms with different prefactors. As a result of the competition of the respective…

This paper concerns classical nonlinear scalar field models on the real line. If the potential is a symmetric double-well, such a model admits static solutions called kinks and antikinks, which are perhaps the simplest examples of…

The deformed model $\tilde{\varphi}^{(6)}$ is introduced based on the $\varphi^4$ model using a deformation functional $F[\varphi]$ including a free parameter $a$. The kink solutions in different sectors and their internal modes are…

We show that the $\theta+$ pentaquark does not exist in the Skyrme model. For the solitons of the theory with topological terms, the standard collective coordinate quantization does not construct the proper low energy effective theory. In…

Solitonic excitations of the one-dimensional quantum droplets are obtained, which smoothly connect vacuum with the flat-top droplet, akin to compactons in classical liquids. These solitons are of the kink type, necessarily residing on a…

We consider the approximate control of solitons in generalized Korteweg-de Vries equations. By introducing a suitable internal bilinear control on the equation, we prove that any soliton is locally null controllable, and moreover, any…

We consider the wave and Klein-Gordon equations on the real hyperbolic space $\mathbb{H}^{n}$ ($n \geq2$) in a framework based on weak-$L^{p}$ spaces. First, we establish dispersive estimates on Lorentz spaces in the context of…

We point out a misleading treatment in the literature regarding to bound-state solutions for the $s$-wave Klein-Gordon equation with exponential scalar and vector potentials. Following the appropriate procedure for an arbitrary mixing of…

We investigate the role that quasinormal modes can play in kink-antikink collisions, via an example based on a perturbation of the $\phi^4$ model. We find that narrow quasinormal modes can store energy during collision processes and return…

Collective coordinates are frequently employed in path integrals to manage divergences caused by fluctuations around saddle points that align with classical symmetries. These coordinates parameterize a manifold of zero modes and more…

A system of semi-discrete coupled nonlinear Schr\"{o}dinger equations is studied. To show the complete integrability of the model with multiple components, we extend the discrete version of the inverse scattering method for the…

We consider a generalized discrete $\phi^4$ model and demonstrate that it can support exact moving kink solutions in the form of tanh with an arbitrarily large velocity. The constructed exact moving solutions are dependent on the specific…

We present a new generalization of the steepest descent method introduced by Deift and Zhou for matrix Riemann-Hilbert problems and use it to study the semiclassical limit of the focusing nonlinear Schroedinger equation with real analytic,…

Evolution of sphalerons in a class of quartic Klein-Gordon models are studied under a growing perturbation. Sphalerons are unstable lump-like solutions that arise from a saddle point between true and false vacua in the energy functional.…

We consider the quantum inverse scattering method for several mixed integrable models based on the rational SU(N) R-matrix with general toroidal boundary conditions. This includes systems whose Hilbert spaces are invariant by the discrete…

In this paper we analyze the scattering process in a two-field model in $(1+1)$-dimensions, with the special property to have several topological solutions: i) one with higher rest mass, characterized by a nested defect (lump inside a…

In this paper, kink scattering in the dimensional reduction of the bosonic sector of a one-parameter family of generalized Wess-Zumino models with three vacuum points is discussed. The value of the model parameter determines the specific…

In both the Gardner equation and its extensions, the non-convex convection bounds the range of solitons / compactons velocities beyond which they dissolve and kink/anti-kink form. Close to solitons barrier we unfold a narrow strip of…

The scattering of a fermion in the background of a smooth step potential is considered with a general mixing of vector and scalar Lorentz structures with the scalar coupling stronger than or equal to the vector coupling. Charge-conjugation…

The convergence of inexact Newton methods is studied for solving generalized equations on Riemannian manifolds by using the metric regularity property, which is also explored. Under appropriate conditions and without any additional…