Related papers: Exact Solutions to Cubic Duffing Equation by Leaf …
We provide an exact algorithm to solve the log-linear continuous (fractional) knapsack problem. The algorithm is based on two lemmas that follow from the application of weak duality theorem and complementary slackness theorem to the linear…
It is well known that second order linear ordinary differential equations with slowly varying coefficients admit slowly varying phase functions. This observation is the basis of the Liouville-Green method and many other techniques for the…
A modified method of functional constraints is used to construct the exact solutions of nonlinear equations of reaction-diffusion type with delay and which are associated with variable coefficients. This study considers a most generalized…
Exact results are derived for 5d SCFTs with holographic duals in Type IIB supergravity. These theories have relevant deformations that flow to linear quiver gauge theories, with the number of nodes large in the large-$N$ limits described by…
In this work an extended elliptic function method is proposed and applied to the generalized shallow water wave equation. We systematically investigate to classify new exact travelling wave solutions expressible in terms of quasi-periodic…
We consider quasi-stationary (travelling wave type) solutions to a general nonlinear reaction-convection-diffusion equation with arbitrary, autonomous coefficients. The second order nonlinear equation describing one dimensional travelling…
In the presented paper known (up to the beginning of 2008) Lie- and non-Lie exact solutions of different $(1+1)$-dimensional diffusion-convection equations of form $f(x)u_t=(g(x)A(u)u_x)_x+h(x)B(u)u_x$ are collected.
We advance an exact, explicit form for the solutions to the fractional diffusion-advection equation. Numerical analysis of this equation shows that its solutions resemble power-laws.
Exact solutions are found to the Dirac equation for a combination of Lorentz scalar and vector Coulombic potentials with additional non-Coulombic parts. An appropriate linear combination of Lorentz scalar and vector non-Coulombic…
We consider a second-order equation of Duffing type. Bounds for the derivative of the restoring force are given which ensure the existence and uniqueness of a periodic solution. Furthermore, the unique periodic solution is asymptotically…
This paper focuses on the numerical solution of initial value problems for fractional differential equations of linear type. The approach we propose grounds on expressing the solution in terms of some integral weighted by a generalized…
Exact solutions are derived for an n-dimensional radial wave equation with a general power nonlinearity. The method, which is applicable more generally to other nonlinear PDEs, involves an ansatz technique to solve a first-order PDE system…
The set of non-linear equations describing the Standard Model kinematics of the top quark antiqark production system in the dilepton decay channel has at most a four-fold ambiguity due to two not fully reconstructed neutrinos. Its most…
Building on a classification of zeros of cubic equations due to the $12$-th century Persian mathematician Sharaf al-Din Tusi, together with Smale's theory of {\it point estimation}, we derive an efficient recipe for computing high-precision…
Governing equations for two-dimensional inviscid free-surface flows with constant vorticity over arbitrary non-uniform bottom profile are presented in exact and compact form using conformal variables. An efficient and very accurate…
New problem is considered that is to find nonlinear differential equations with special solutions. Method is presented to construct nonlinear ordinary differential equations with exact solution. Crucial step to the method is the assumption…
Fractional wave equation arises in different type of physical problems such as the vibrating strings, propagation of electro-magnetic waves, and for many other systems. The exact analytical solution of the fractional differential equation…
The closed form solution is found for the fully nonlinear dynamics of the gyroscope with a fixed point at the tip. The solution is found by using Cardano's formulae to factor a cubic, in the case where all roots are known to be real. From…
In this article we study solutions to second order linear difference equations with variable coefficients. Under mild conditions we provide closed form solutions using finite continued fraction representations. The proof of the results are…
We construct a two-parameter family of explicit solutions to the cubic wave equation on $\mathbb{R}^{1+3}$. Depending on the value of the parameters, these solutions either scatter to linear, blow-up in finite time, or exhibit a new type of…