I think that speaks more to english-language scholarship on the Italian front more than anything; Italian scholarship might be more extensive. However, I'm sure an english-language history of the Italian front will discuss the Piave in detail. indeed, the rout at Caporetto was definitively stopped along the line of the Piave; although the propagandistic and nationalist elements of the battle were subsequently played up, the battle most certainly marked a definitive turning point in the war. Both Italy and Austria-Hungary weren't in very good shape as they entered the war, and things only got worse as the conflict went on. Both suffered from crippling inefficiencies. However, only Austria-Hungary was coming apart at the seams of its various ethnicities, while Italy, although also beset by unrest, had an easier time restoring morale and rallying to victory.

The rout at Caporetto was more then a military disaster: it finally exposed, without a trace of doubt, the incompetence the Italian general staff. In fact, only over the course of the whole morning of the 25th of October did the Italian government and general staff became fully aware of the fact that the Austro-German offensive of the previous day had broken through the line in multiple places. To make matters worse, General Luigi Cadorna, the Italian Army's Chief of Staff, delayed countermeasures for two full days for no clear reason (perhaps he was waiting for divine intervention, or more ignobly was waiting to see Parliament's reaction before acting).

The success of the offensive surprised even the Germans, who recalled the reinforcements they had sent their Austrian allies in order to redeploy them on the western front. Luckily, poor communication along lines of command on behalf of the unsupported Austro-Hungarians delayed the advance, allowing Cadorna the time to set up defenses on the Tagliamento River (the prewar border) on the 27th of October. Cadorna's beleaguered forces would find little solace in the respite that Austro-Hungarian incompetence allowed them: On the evening of the 28th of October, the Austrians resumed their offensive. To make the dire situation worse, significant portions of Cadorna's already limited brain capacity were directed towards the Parliament in Rome, where on the 25th of October the wartime "National Unity" coalition, prompted by the defeat at Caporetto, voted no confidence with regards to the meek Prime Minister Boselli. Boselli's own Minister of the Interior, the conniving Sicilian Vittorio Emanuele Orlando, was confirmed as Premier on October 30th, when the battle of the Tagliamento was in full swing. Although Vittorio Emanuele Orlando promptly telegraphed Cadorna expressing his respect and full confidence in his ability, Orlando had already proposed Cadorna's removal in the days prior to his elevation to Premier.

Orlando met with the French and British Prime ministers on the Ligurian resort of Rapallo on November 6th, where a condition for sending the Italian Army reinforcements was set: Cadorna had to be removed from command in favor of King Victor Emmanuel's cousin, the Duke of Aosta, commander of the Italian 3d Army. Up until the battle of Caporetto the Italian 3d Army had been undefeated and Aosta had been a popular choice to succeed Cadorna for some time. But King Victor Emmanuel conceded to France and England's terms on the sole condition that he be able to pick Cadorna's successor (i.e., be allowed to pick anyone but his cousin). The concession was made, and on November 8th, Lt. General Armando Diaz, head of the 3d Army 23d Corps was elevated to the rank of Chief of Staff, while Cadorna was "promoted" to the Italian representative to the Allies' "Military Council" in Versailles.

Armando Diaz had been awarded a medal for bravery at Caporetto, but was otherwise an unknown subordinate of Aosta's. The reason for his elevation can be attributed to the same reason Cadorna kept his job for so long: King Victor Emmanuel was jealous of the success and popularity of his cousin, who was not only a competent general, but was also a well spoken gentleman fluent in French and English, making him popular with the Franco-British high command.

To his credit, Diaz immediately occupied the high ground on Mount Grappa as well as the more obvious Piave River. Recent draftees, almost all born in 1899, were rapidly and seamlessly rushed to the front to replenish the depleted lines. The contraction of the front along the Mountain-River-Sea line allowed the Italian Army to compress its thinning regiments and mount a successful defense. As the Austro-Hungarians would not attack over the ice-cold river flowing through the flat Venetian plain, so all through November they attempted to attack up and around through the Asolone, Grappa, Spinoncia and Pallone mountains.

Diaz made a number of critical decisions that helped turn the tide, one of which was to do nothing at all. By distancing himself and the general staff from the day-to-day operations of the army and giving his subordinates the prerogative to attack and defend across the mountain valleys on their own initiative, the numerically inferior Italian forces were able to defend the front with minimal losses in the first "mobile" battle of the Italian front. Subordinate generals were shocked to find out just how effective their men were. General Gaetano Giardino of the 4th army said of the "Kids of '99" who had replenished his regiments, "True Soldiers [...] who not by virtue of the actions by commanders or the government, nor for favorable military conditions, but they alone and their officers found moral conscience and valor" (the translation, by me, is kind of circuitous but you get the idea).

Of course, general Giardino's explanation is a little too romantic. Rather, the Austro-Hungarians were facing fresh troops that were finally freed from the stiff constraints of the leadership's antiquated human-wave tactics. Plus, they just didn't have the ground in their favor: in order to continue the attack, their options were up the side of a mountain, through narrow valleys, or over a river into a flat plain (i.e., either up a hill or over a wide plain of open ground; I'm not a military historian, but I don't think I need to be to understand those are very unappealing scenarios). In addition, the positional freedom granted by Diaz was especially useful for the specialist Alpine regiments, who took up exemplary defensive positions.

On November 25th, the last Austro-Hungarian assault saw fifteen divisions charge up Mt. Grappa, repulsed by twelve numerically inferior Italian divisions. Both sides then dug in for the winter, although skirmishes continued to flair up all through December. While the defeat of Russia in the east saw the Austro-Hungarians free up more divisions for Italy in December 1917, the Italian Army was also reinforced by six French and five British divisions which took up positions as rearguard allowing the entire Italian force to be concentrated along the front.

Having been somewhat detached from the high command before his appointment, general Diaz also had a good grasp of the situation on the ground. Diaz worked all through the winter of 1917-1918 to build up his army's morale, increasing the amount of soldiers' paid leave time to the rear, and assigning drafted artists and writers were to work in a new army propaganda office, nicknamed "P-Division." The "P-Division" among other things published a "Trench Newspaper;" designed to lift the Army's spirits by framing their soldiers's struggle as part of a wider European conflict, and encourage fraternization between Italian soldiers and the Franco-British rearguard. On the other hand, the tired Austro-Hungarian army saw itself increasingly restless among ethnic lines, even among the officers. With the army absent on Imperial territory for some time, the Austro-Hungarian Empire began to feel ethnic tension as well, catalyzing instability and crippling industrial and agricultural production. Just as the Austria-Hungary was preparing their spring offensive, seven divisions had to be recalled from the front to restore order within the Empire.

The deepening divisions within the Austrian command also impacted their decision making. Unable to decide if their spring offensive should target Mt. Grappa or the Piave River, the disastrous decision was made to split forces and attack both. Commencing on the 15th of June, the attack up the side of the mountain was disastrous (also in part because dissatisfied deserters had betrayed the location of the attack) while the attack over the River Piave made initial gains, torrential spring rains swelled the River Piave, destroying the Austro-Hungarian bridgeheads, isolating the attacking force. On the 23d of June both prongs of the attack were completely depleted, and the Imperial forces withdrew.

Diaz actually needlessly delayed his counterattack, hoping to receive American reinforcements. However, once they were finally denied (save for a token regiment) he was quick make up ground. Between July and October, the Italian army made spectacular gains, as Imperial soldiers deserted the army en masse and the empire collapsed. On October 28th, Austria-Hungary asked for an armistice.

So in short, after the battle of the Piave the Austro-Hungarian army collapsed, paving the way for Italian victory.