Exact solutions to the double sinh-gordon equation by the tanh method and a variable separated ODE method

AbstractNew exact travelling wave solutions for the double sinh-Gordon equation and its generalized form are formally derived by using the tanh method and the variable separated ODE method. The Painlevé property v = eu is employed to support the tanh method in deriving exact solutions. The work emphasizes the power of the methods in providing distinct solutions of different physical structures

Cosmic bubble and domain wall instabilities I: parametric amplification of linear fluctuations

This is the first paper in a series where we study collisions of nucleated bubbles taking into account the effects of small initial (quantum) fluctuations in a fully 3+1-dimensional setting. In this paper, we consider the evolution of linear fluctuations around highly symmetric though inhomogeneous backgrounds. We demonstrate that a large degree of asymmetry develops over time from tiny fluctuations superposed upon planar and SO(2,1) symmetric backgrounds. These fluctuations arise from zero-point vacuum oscillations, so excluding them by enforcing a spatial symmetry is inconsistent in a quantum treatment. We consider the limit of two colliding planar walls, with fluctuation mode functions characterized by the wavenumber transverse to the collision direction and a longitudinal shape along the collision direction $x$, which we solve for. Initially, the fluctuations obey a linear wave equation with a time- and space-dependent mass $m_{eff}(x,t)$. When the walls collide multiple times, $m_{eff}$ oscillates in time. We use Floquet theory to study the fluctuations and generalize techniques familiar from preheating to the case with many coupled degrees of freedom. This inhomogeneous case has bands of unstable transverse wavenumbers $k_\perp$ with exponentially growing mode functions. From the detailed spatial structure of the mode functions in $x$, we identify both broad and narrow parametric resonance generalizations of the homogeneous $m_{eff}(t)$ case of preheating. The unstable $k_\perp$ modes are longitudinally localized, yet can be described as quasiparticles in the Bogoliubov sense. We define an effective occupation number to show they are created in bursts for the case of well-defined collisions in the background. The transverse-longitudinal coupling accompanying nonlinearity radically breaks this localized particle description, with nonseparable 3D modes arising.Comment: 37 pages + references, 20 figures, submitted to JCA

Quantum transfer-matrices for the sausage model

In this work we revisit the problem of the quantization of the two-dimensional O(3) non-linear sigma model and its one-parameter integrable deformation -- the sausage model. Our consideration is based on the so-called ODE/IQFT correspondence, a variant of the Quantum Inverse Scattering Method.The approach allowed us to explore the integrable structures underlying the quantum O(3)/sausage model. Among the obtained results is a system of non-linear integral equations for the computation of the vacuum eigenvalues of the quantum transfer-matrices.Comment: 89 pages, 10 figures, v2: misprints corrected, some comments added, v3, v4: minor corrections, references adde

Kink dynamics in the MSTB model

Producción CientíficaIn this paper kink scattering processes are investigated in the Montonen–Sarker–Trullinger–Bishop (MSTB) model. The MSTB model is in fact a one-parametric family of relativistic scalar field theories living in a one-time one-space Minkowski space-time which encompasses two coupled scalar fields. Among the static solutions of the model two kinds of topological kinks are distinguished in a precise range of the family parameter. In that regime there exists one unstable kink exhibiting only one non-null component of the scalar field. Another type of topological kink solutions, stable in this case, includes two different kinks for which the two components of the scalar field are non-null. Both one-component and two-component topological kinks are accompanied by their antikink partners. The decay of the unstable kink to one of the stable solutions plus radiation is numerically computed. The pair of stable two-component kinks living respectively on upper and lower semi-ellipses in the field space belongs to the same topological sector in the configuration space and provides an ideal playground to address several scattering events involving one kink and either its own antikink or the antikink of the other stable kink. By means of numerical analysis we shall find and describe interesting physical phenomena. Bion (kink–antikink oscillations) formation, kink reflection, kink–antikink annihilation, kink transmutation and resonances are examples of these types of events. The appearance of these phenomena emerging in the kink–antikink scattering depends critically on the initial collision velocity and the chosen value of the coupling constant parametrizing the family of MSTB models.MINDECO grant MTM2014-57129-C2-1-P and Junta de Castilla y León grants VA057U16 and BU229P18