The generalized magma equation, in which dispersion and nonlinearity are coupled together in a manner reminiscent of the Harry-Dym equation, is solved to indicate both periodic and aperiodic implicit solitary wave solutions. It is argued that the presence of an additional spatial derivative in the magma equation also permits explicit solitary wave solutions, a feature not shared by the Harry-Dym equation.
It is well known that much of the geological formations are caused by thermal activities within the mantle of the earth. It may even be speculated that mountain chains and volcanoes result from the interactions of large masses of molten rock rising to the surface under enormous temperatures and pressures. On the basis of modes of origin, many of which can be seen operating today, early uniformitarian geologists came to recognize three basic types of rock: igneous, sedimentary and metamorphic. The most familiar igneous rock to the nongeologist is granite. The molten material, or magma, that turns into igneous rocks, comes from great depths within the earth, where temperatures are very high. This material may reach the earth's surface through cracks and fissures in the crust and then cool to form extrusive, or volcanic, igneous rock. Additionally, it turns out that the propagation of magma may be traced via plate tectonics and orogenesis to the formation of mountain chains. Orogeny, or mountain building, is a complex process that is only partly understood; nonetheless, the simple idea that plates move, carrying continents with them, points to one mechanism of orogenesis; the collision of two continents. The welded boundaries of subducting tectonic plates, or sutures, result in one continent overriding the igneous are associated with the subduetion zone. Consequently, magma rises into the continental crust. Some of the magma reaches the surface, forming a chain of volcanoes that elevate the crust, often forming mountain peaks. Some magma also cools within the crust, forming plutons of igneous rock. Further details may be excavated from Stanley t. Surprisingly, the search for appropriate mathematical models to describe the above complex phenomena began only recently. Since 1974, several researchers have proposed model equations for the migrating motion of molten rock through a deformable, solid rock matrix 2-7. The corresponding flow