Related papers: Burgers' equation in non-commutative space-time
In previous work, we developed quantum physics on the Moyal plane with time-space noncommutativity, basing ourselves on the work of Doplicher et al.. Here we extend it to certain noncommutative versions of the cylinder, $\mathbb{R}^{3}$ and…
We described the $q$-deformed phase space. The $q$-deformed Hamilton eqations of motion are derived and discussed. Some simple models are considered.
The q-deformation of harmonic oscillators is shown to lead to q-nonlinear vibrations. The examples of q-nonlinearized wave equation and Schr\"odinger equation are considered. The procedure is generalized to broader class of nonlinearities…
Burgers' equation with fixed Dirichlet boundary conditions is considered on generic bounded intervals. By using the Hopf-Cole transformation and the exact operational solution recently established for linear reaction-diffusion equations…
A fractional time derivative is introduced into the Burger's equation to model losses of nonlinear waves. This term amounts to a time convolution product, which greatly penalizes the numerical modeling. A diffusive representation of the…
This manuscript studies the numerical solution of the time-fractional Burgers-Huxley equation in a reproducing kernel Hilbert space. The analytical solution of the equation is obtained in terms of a convergent series with easily computable…
In this paper we present a system of two nonlinear partial differential equations of the second order, depending on the time and one spatial coordinate. It can be written as a system of two Burgers equations, which allows one to immediately…
We consider Burgers equation with transverse viscosity $$\partial_tu+u\partial_xu-\partial_{yy}u=0, \ \ (x,y)\in \mathbb R^2, \ \ u:[0,T)\times \mathbb R^2\rightarrow \mathbb R.$$ We construct and describe precisely a family of solutions…
We consider localized soliton-like solutions in the presence of a stable scalar condensate background. By the analogy with classical mechanics, it can be shown that there may exist solutions of the nonlinear equations of motion that…
We study conservation laws and potential symmetries of (systems of) differential equations applying equivalence relations generated by point transformations between the equations. A Fokker-Planck equation and the Burgers equation are…
N-dimensional B\"acklund transformation (BT), Cole-Hopf transformation and Auto-B\"acklund transformation (Auto-BT) of n-dimensional Burgers system are derived by using simplified homogeneous balance (SHB). By the Auto-BT, another solution…
We carry out the construction of some ill-posed multiplicative stochastic heat equations on unbounded domains. The two main equations our result covers are, on the one hand the parabolic Anderson model on $\mathbf{R}^3$, and on the other…
In this paper we consider a class of Burgers equation. We propose a new method of investigation for existence of classical solutions.
In this article, the new exact travelling wave solutions of the time-and space-fractional KdV-Burgers equation has been found. For this the fractional complex transformation have been implemented to convert nonlinear partial fractional…
In the last decades, noncommutative spacetimes and their deformed relativistic symmetries have usually been studied in the context of field theory, replacing the ordinary Minkowski background with an algebra of noncommutative coordinates.…
Thermodynamic formalism for rotating black holes, characterized by noncommutative and quantum corrections, is constructed. From a fundamental thermodynamic relation, equations of state and thermodynamic response functions are explicitly…
We study classical scalar field theories on noncommutative curved spacetimes. Following the approach of Wess et al. [Classical Quantum Gravity 22 (2005), 3511 and Classical Quantum Gravity 23 (2006), 1883], we describe noncommutative…
This work explores the set of coupled partial differential equations of the Einstein equations yielding vacuum solutions in the original Alcubierre warp drive metric with the cosmological constant. It is shown that under an appropriate…
This paper treats nonlinear wave current interactions in their simplest form, as an overtaking collision. In one spatial dimension, the paper investigates the collision interaction formulated as an initial value problem of a Burgers bore…
We consider the Burgers equation on $H=L^2(0,1)$ perturbed by white noise and the corresponding transition semigroup $P_t$. We prove a new formula for $P_tD\varphi$ (where $\varphi:H\to\R$ is bounded and Borel) which depends on $\varphi$…