  Existence and admissibility of $\delta$-shock type solution is discussed for
the following nonconvex strictly hyperbolic system arising in studues of
plasmas: \pa_t u + \pa_x \big(\Sfrac{u^2+v^2}{2} \big) &=0 \pa_t v
+\pa_x(v(u-1))&=0. The system is fully nonlinear, i.e. it is nonlinear with
respect to both variables. The latter system does not admit the classical
Lax-admissible solution to certain Riemann problems. By introducing complex
valued corrections in the framework of the weak asymptotic method, we show that
an compressive $\delta$-shock type solution resolves such Riemann problems. By
letting the approximation parameter to zero, the corrections become real valued
and we obtain a $\delta$-type solution concept. In the frame of that concept,
we can show that every $2\times 2$ system of conservation laws admits
$\delta$-type solution.
