Results 31 to 40 of about 1,885 (105)

Exact solutions of the Kudryashov–Sinelshchikov equation [PDF]

Applied Mathematics and Computation, 2010
The Kudryashov-Sinelshchikov equation for describing the pressure waves in liquid with gas bubbles is studied. New exact solution of this equation are found. Modification of truncated expansion method is used for obtaining exact solution of this equation.
openaire   +3 more sources

Evolution of spherical cavitation bubbles: parametric and closed-form solutions [PDF]

, 2016
We present an analysis of the Rayleigh-Plesset equation for a three dimensional vacuous bubble in water. In the simplest case when the effects of surface tension are neglected, the known parametric solutions for the radius and time evolution of the ...
Haret C. Rosu, Kamke E., Plesset M. S., Polyanin A. D., Stefan C. Mancas, Whittaker E. T.   +5 more
core   +3 more sources

A KdV-like advection-dispersion equation with some remarkable properties [PDF]

, 2012
We discuss a new non-linear PDE, u_t + (2 u_xx/u) u_x = epsilon u_xxx, invariant under scaling of dependent variable and referred to here as SIdV. It is one of the simplest such translation and space-time reflection-symmetric first order advection ...
Abhijit Sen, Anantanarayanan Thyagaraja, Benney, Dilip P. Ahalpara, Govind S. Krishnaswami, Korteweg, Kudryashov, Miura, Randrt, Ryabov, Thyagaraja, Washimi, Yomosa, Zabusky   +13 more
core   +1 more source

The plethora of explicit solutions of the fractional KS equation through liquid–gas bubbles mix under the thermodynamic conditions via Atangana–Baleanu derivative operator

Advances in Difference Equations, 2020
Novel explicit wave solutions are constructed for the Kudryashov–Sinelshchikov (KS) equation through liquid–gas bubbles mix under the thermodynamic conditions.
Chen Yue, Mostafa M. A. Khater, Raghda A. M. Attia, Dianchen Lu   +3 more
doaj   +1 more source

Nonlocal Symmetry Analysis and Conservation Laws to an Third-order Burgers Equation [PDF]

, 2015
Third-order Burger equationNonlocal 11 symmetry analysisLinearizationmultiplier 12 approachConservation lawsThe nonlocal residual symmetry related to truncated Painlevé expansion of third-order Burgers equation is performed.

core   +1 more source

Exact meromorphic stationary solutions of the real cubic Swift-Hohenberg equation [PDF]

, 2012
We show that all meromorphic solutions of the stationary reduction of the real cubic Swift-Hohenberg equation are elliptic or degenerate elliptic. We then obtain them all explicitly by the subequation method, and one of them appears to be a new elliptic ...
Berg, Berg, Briot, Chazy, Chiang, Conte, Conte, Conte, Cross, Cross, Eremenko, Eremenko, Eremenko, Hayman, Hille, Hoyle, Jones, Kudryashov, Kwapisz, Laine, Lega, Longhi, Maruno, Musette, Peletier, Santra, Smets, Swift, Yee   +28 more
core   +2 more sources

Nonlinear wave solutions of the Kudryashov–Sinelshchikov dynamical equation in mixtures liquid-gas bubbles under the consideration of heat transfer and viscosity

Journal of Taibah University for Science, 2019
In this research, we constructed the exact travelling and solitary wave solutions of the Kudryashov–Sinelshchikov (KS) equation by implementing the modified mathematical method.
Aly R. Seadawy, Mujahid Iqbal, Dianchen Lu   +2 more
doaj   +1 more source

Traveling Wave Solutions and Infinite‐Dimensional Linear Spaces of Multiwave Solutions to Jimbo‐Miwa Equation

Abstract and Applied Analysis, Volume 2014, Issue 1, 2014., 2014
The traveling wave solutions and multiwave solutions to (3 + 1)‐dimensional Jimbo‐Miwa equation are investigated in this paper. As a result, besides the exact bounded solitary wave solutions, we obtain the existence of two families of bounded periodic traveling wave solutions and their implicit formulas by analysis of phase portrait of the ...
Lijun Zhang, C. M. Khalique, Weiguo Rui
wiley   +1 more source

Dynamics of the Rayleigh-Plesset equation modelling a gas-filled bubble immersed in an incompressible fluid [PDF]

, 2016
Temporal dynamics of gas-filled spherical bubbles are often described using the Rayleigh-Plesset equation, a special case of the Navier-Stokes equations that describes the oscillations of a spherical cavity in an infinite incompressible fluid.
Van Gorder, Robert A.
core   +2 more sources

Extended equation for description of nonlinear waves in liquid with gas bubbles

, 2013
Nonlinear waves in a liquid with gas bubbles are studied. Higher order terms with respect to the small parameter are taken into account in the derivation of the equation for nonlinear waves.
Kudryashov, Nikolai A., Sinelshchikov, Dmitry I.   +1 more
core   +1 more source