0000000000502408
AUTHOR
Tommaso Brugarino
Integrating the Kadomtsev-Petviashvili Equation in the 1+3 Dimensions VIA the Generalised Monge-Ampère Equation: An Example of Conditioned Painlevé Test
Travelling waves for two coupled Korteweg-De Vries
Exact solutions of the Zakharov equations
Traveling Waves of two Coupled Nonlinear Diffusion Convection Equations
Travelling wave solutions of nonlinear equations using the Auxiliary Equation Method
In this paper we obtain travelling wave solutions of nonlinear partial differential equations starting from a different reducible hyperelliptic equation as an auxiliary equation which does not appear in any other paper. We point out that all the cases, to our knowledge, considered in the literature are included in this paper, so our work exhausts all the reducible cases of the hyperelliptic equation to the genus one.
Painlev\'{e} analysis for a generalized nonlinear Schr\"{o}dinger equation
Nonlinear Kelvin waves on a quantized vortex line in superfluid helium
In this paper we show an exact solution (Kelvin wave) of an approximated dynamical equation for a quantized vortex line in helium superfluid at finite temperature. It is shown that the applied heat flux interacts with the vortex line, and the amplitude of the Kelvin wave can grow (the so-called Donnelly instability) or decrease according with the mutual direction between heat flux and wave vector.
Waves on a vortex filament: exact solutions of dynamical equations
In this paper we take into account the dynamical equations of a vortex filament in superfluid helium at finite temperature (1 K < T < 2.17 K) and at very low temperature, which is called Biot-Savart law. The last equation is also valid for a vortex tube in a frictionless, unbounded and incompressible fluid. Both the equations are approximated by the Local Induction Approximation (LIA) and Fukumoto's approximation. The obtained equations are then considered in the extrinsic frame of reference, where exact solutions (Kelvin waves) are shown. These waves are then compared one to each other in terms of their dispersion relations in the frictionless case. The same equations are then investigated…
A direct method to find solutions of some type of coupled Korteweg-de Vries equations using hyperelliptic functions of genus two
Abstract We suggest how one can obtain exact solutions of some type of coupled Korteweg–de Vries equations by means of hyperelliptic functions of genus two.
Exact solutions of nonlinear differential equations using the abelian equation of the first type
Solutions of some coupled Korteweg-de Vries equations in terms of hyperelliptic functions of genus two
Group analysis and similarity solutions of the compressible boundary layer equations
In this paper the application of Lie's methods to the equations of the laminar boundary layer is discussed. The momentum and energy equations in Prandtl's form are considered for a steady, viscous, compressible laminar flow with non zero pressure gradient, variable viscosity and thermal conductivity. Group analysis yields similarity solutions for given pressure distributions and particular values of the invariance group parameters (group classification). Crocco's transformation is obtained for the infinite-dimensional group of the Lie's algebra admitted by the equations.
Singularity analysis and integrability for a HNLS equation governing pulse propagation in a generic fiber optics
Abstract Taking into account many developments in fiber optics communications, we propose a higher nonlinear Schrodinger equation (HNLS) with variable coefficients, more general than that in [R. Essiambre, G.P. Agrawal, Opt. Commun. 131 (1996) 274], which governs the propagation of ultrashort pulses in a fiber optics with generic variable dispersion. The study of this equation is performed using the Painleve test and the zero-curvature method. Also, we prove the equivalence between this equation and its anomalous integrable counterpart (the so-called Sasa–Satsuma equation). Finally, in view of its physical relevance, we present a soliton solution which represents the propagation of ultrasho…
Some Exact Solutions of two Coupled Nonlinear Diffusion Convection Equations
The aim of the note is to apply a slightly modified version of the truncated Painlevè test to obtain a class of solutions of the system of two coupled nonlinear partial differential equations. These solutions are expressed in term of the Airy functions. We also give the travelling wave solutions, expressed in term of the trigonometric and hyperbolic functions. The aim of the note is to apply a slightly modified version of the truncated Painlevè test to obtain a class of solutions of the system of two coupled nonlinear partial differential equations. These solutions are expressed in term of the Airy functions. We also give the travelling wave solutions, expressed in term of the trigonometric…
Painlevé analysis and reducibility to the canonical form for the nonlinear generalized Schreodinger equation
Some exact solutions of the two dimensional Bussinesq equation
Integrability of an inhomogeneous nonlinear Schrödinger equation in Bose–Einstein condensates and fiber optics
In this paper, we investigate the integrability of an inhomogeneous nonlinear Schrödinger equation, which has several applications in many branches of physics, as in Bose-Einstein condensates and fiber optics. The main issue deals with Painlevé property (PP) and Liouville integrability for a nonlinear Schrödinger-type equation. Solutions of the integrable equation are obtained by means of the Darboux transformation. Finally, some applications on fiber optics and Bose-Einstein condensates are proposed (including Bose-Einstein condensates in three-dimensional in cylindrical symmetry).