‎hensel [k‎. ‎hensel‎, ‎deutsch‎. ‎math‎. ‎verein‎, ‎{6} (1897), ‎83-88.] discovered the $p$-adic number as a‎ ‎number theoretical analogue of power series in complex analysis‎. ‎fix ‎a prime number $p$‎. ‎for any nonzero rational number $x$‎, ‎there‎ ‎exists a unique integer $n_x inmathbb{z}$ such that $x = ‎frac{a}{b}p^{n_x}$‎, ‎where $a$ and $b$ are integers not divisible by ‎$p$‎. ‎then $|x...

We consider the existence of a dynamically stable soliton in the one-dimensional cubic-quintic nonlinear Schrödinger model with strong cubic nonlinearity management for periodic and random modulations. We show that the predictions of the averaged cubic-quintic nonlinear Schrödinger (NLS) equation and modified variational approach for the arrest of collapse coincide. The analytical results are c...

We consider a cubic nonlinear wave equation with highly oscillating cubic coefficient and wave packet initial data. Using a regularization step of the initial data, we give a low regularity justification of the Nonlinear Schrödinger equation as the envelope equation.

We present the results of a first-principles study on BaF2 in its stable (cubic) and high-pressure phases. A linear combination of atomic orbitals approach in the framework of density functional theory is employed for total energy calculations in cubic, orthorhombic and hexagonal phases of BaF2. A fitting of the energy surface to the equation of state yields the lattice constant and the bulk mo...

we have developed a three level implicit method for solution of the helmholtz equation. using the cubic spline in space and nite dierence in time directions. the approach has been modied to drive numerov type nite dierence method. the method yield the tri- diagonal linear system of algebraic equations which can be solved by using a tri-diagonal solver. stability and error estimation of the...

In this paper, we obtain the general solution and the generalized Ulam-Hyers stability of the cubic and quartic functional equation 4(f(3x + y) + f(3x− y)) = −12(f(x + y) + f(x− y)) + 12(f(2x + y) + f(2x− y))− 8f(y)− 192f(x) + f(2y) + 30f(2x).