We formally derive the simplest possible periodic wave structure consistent with time-periodic sound wave propagation in the 3 × 3 nonlinear compressible Euler equations. The construction is based on identifying the simplest periodic pattern with the property that compression is counter-balanced by rarefaction along every characteristic. Our derivation leads to an explicit description of shock-...

A systems approach model for prostate cancer in prostate duct, as a sub-system of the organism is developed. It is accomplished in two steps. First this research work starts with a nonlinear system of coupled Fokker-Plank equations which models continuous process of the system like motion of cells. Then extended to PDEs that include discontinuous processes like cell mutations, proliferation and...

We obtain KSS, Strichartz and certain weighted Strichartz estimate for the wave equation on (R, g), d ≥ 3, when metric g is non-trapping and approaches the Euclidean metric like 〈x〉 with ρ > 0. Using the KSS estimate, we prove almost global existence for quadratically semilinear wave equations with small initial data for ρ > 1 and d = 3. Also, we establish the Strauss conjecture when the metric...

We obtain KSS, Strichartz and certain weighted Strichartz estimates for the wave equation on (R, g), d ≥ 3, when metric g is non-trapping and approaches the Euclidean metric like 〈x〉 with ρ > 0. Using the KSS estimate, we prove almost global existence for quadratically semilinear wave equations with small initial data for ρ > 1 and d = 3. Also, we establish the Strauss conjecture when the metri...

A foundation theory of quantum mechanics is proposed in another paper that governs state reduction in general, and particle localization in particular. The theory is based on a set of four rules called the nRules. In the present paper the nRules and the nRule equations are shown to be Lorentz invariant. The details of a non-local, space-like collapse of a relativistic wave function depend on th...

In this work, an efficient approximation scheme has been proposed for getting accurate approximate solution of nonlinear partial differential equations with constant or variable coefficients satisfying initial conditions in a series exponential instead algebraic function independent variables. As consequence: i) the convergence found to be faster than same obtained by few other methods and ii) ...

Einstein assumed in his Special Theory of Relativity that Maxwell’s equations, including Faraday’s law and the AmpereMaxwell equation, were invariant in any inertial frame, and that the Lorentz transformation equations must be used when two inertial frames were in relative motion. Starting with a modification of the Ampere-Maxwell equation that allows for two observers of the magnetic field in ...

Transition layers arising from square-wave-like periodic solutions of a singularly perturbed delay differential equation are studied. Such transition layers correspond to heteroclinic orbits connecting a pair of equilibria of an associated system of transition layer equations. Assuming a monotonicity condition in the nonlinearity, we prove these transition layer equations possess a unique heter...

In this paper, an application of homotopy perturbation method is appliedto nding the solutions of the seven-order Sawada-Kotera (sSK) and a Lax'sseven-order KdV (LsKdV) equations. Then obtain the exact solitary-wave so-lutions and numerical solutions of the sSK and LsKdV equations for the initialconditions. The numerical solutions are compared with the known analyticalsolutions. Their remarkabl...