We study a fluid jet descending through stratified surroundings at low Reynolds number in Hele-Shaw flow. The jet buckles and overturns inside a conduit of entrained fluid which supports smooth or unstable traveling waves. A model of the recirculating flow within the conduit shows that buckling and waves arise from Kelvin-Helmholtz instabilities and quantitatively accounts for the main experime...

We consider the initial value problem for generalized Fornberg-Whitham equation, which consists of p-order nonlinear advection term and nonlocal dispersion term. In case p=2, we study sufficient conditions blow-up solutions some relations to Burgers equation. Also, p?5, show global existence with small data.

Abstract: A new periodic wave solution in terms of Riemann theta functions to the elliptic equation is presented, then by using this solution and the improved generalized F-expansion method, some exact solutions in terms of Riemann theta functions to the KdV-Burgers-Kuramoto(KBK) equation are obtained with the aid of Mathematica, their properties and profiles are displayed in their figures. To ...

The conditions for a generalized Burgers equation which a priori involves nine arbitrary functions of one, or two variables to allow an infinite dimensional symmetry algebra are determined. Though this algebra can involve up to two arbitrary functions of time, it does not allow a Virasoro algebra. This result confirms that variable coefficient generalizations of a non-integrable equation should...

There are a great many proteins that localize to and collectively generate curvature in biological fluid membranes. We study changes in the topology of fluid membranes due to the presence of highly anisotropic, curvature-inducing proteins. Generically, we find a surprisingly rich phase diagram with phases of both positive and negative Gaussian curvature. As a concrete example modeled on experim...

Thermodynamics of small systems has become an important field of statistical physics. Such systems are driven out of equilibrium by a control, and the question is naturally posed how such a control can be optimized. We show that optimization problems in small system thermodynamics are solved by (deterministic) optimal transport, for which very efficient numerical methods have been developed, an...

In the theoretical investigation, directly seeking exact solutions for nonlinear partial differential equations has become one of the central themes of perpetual interest in mathematical physics. Nonlinear wave phenomena appear in many fields, such as fluid mechanics, biomathematics, plasma physics, optical fibers, chemical physics, and other areas of engineering. These nonlinear phenomena are ...

The exact traveling wave solutions of the nonlinear variable coefficients Burgers-Fisher equation and the generalized Gardner equation with forced terms can be found in this article using the generalized ( ′ G )-expansion method. As a result, hyperbolic, trigonometric and rational function solutions with parameters are obtained. When these parameters are taken special values, the solitary wave ...

Abstract We propose a polynomial-based numerical scheme for solving some important nonlinear partial differential equations (PDEs). In the proposed technique, temporal part is discretized by finite difference method together with ? -weighted scheme. Then, approximation of spatial unknown function and its derivatives, we use mixed approach based on Lucas Fibonacci polynomials. With help these ap...