Novel solitons in the (2+1)-dimensional Heisenberg spin chain via generalized conformable derivatives. [PDF]
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Nonlinear Analysis: Theory, Methods & Applications, 1996The well posedness of the abstract Cauchy problem \[ u'(t) = Au(t) + \int^t_{t_0} K \bigl( t,s,u(s) \bigr) ds + f(t), \quad u(t_0) = u_0 \] is studied, \(A\) denoting a linear Hille-Yosida operator in the Banach space \((X,II \cdot II)\). The paper consists of different Sections, and includes the proof of various theorems. The last Section refers to an
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Oscillation Properties of Nonlinear Hyperbolic Equations
SIAM Journal on Mathematical Analysis, 1984The authors derive a number of new oscillation criteria for hyperbolic equations. First of all, three theorems are proved, giving sufficient conditions for oscillation of solutions of the characteristic initial value problem \[ (2.2)\quad u_{xy}+c(x,y,u)=f(x,y),\quad u_ x(x,0)=g(x),\quad u_ y(0,y)=h(y), \] in an unbounded region contained in the ...
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CENTERED DIFFERENCE SCHEMES FOR NONLINEAR HYPERBOLIC EQUATIONS
Journal of Hyperbolic Differential Equations, 2004A hierarchy of centered (non-upwind) difference schemes is identified for solving hyperbolic equations. The bottom of the hierarchy is the classical Lax–Friedrichs scheme, which is the least accurate in computation, and the top of the hierarchy is the FORCE scheme, which is the optimal scheme in the family.
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